The 172 MEL? Did you have one? I doubt it.
Actually, I do carry the POHs, MELs, full Maintenance Manuals (both airframe & powerplant) for the aircraft I fly on my tablets (tablets plural, for redundancy). I’ve actually read them as well. The POH doesn't mention that the attitude indicator's gyro will run for 15 minutes after losing vacuum, but the MM does. As expected it gets lazier and less responsive over time, but I'd already written off the vacuum-powered gauges as soon as both vacuum pump idiot lights illuminated.
I'm extremely anal when it comes to the aircraft I fly, as the field's mechanic and avionics shop can attest to. My CFI discovered my anal-ness on a night cross country when some of the instrument lights weren't operating as
he expected. I opened the Maintenance Manual on the iPad and they were working perfectly
as designed. Terrible design, but indeed working to factory specs.
If not, did you comply with the requirements of 91.213?
“(3) The inoperative instruments and equipment are—
(i) Removed from the aircraft, the cockpit control placarded, and the maintenance recorded in accordance with §43.9 of this chapter; or
(ii) Deactivated and placarded “Inoperative.” If deactivation of the inoperative instrument or equipment involves maintenance, it must be accomplished and recorded in accordance with part 43 of this chapter;
I grounded & pulled the aircraft off the schedule immediately after the flight. And yes, I'm anal enough to carry a P-Touch in my car and did put INOP stickers on the affected gauges, along with a note tied with safety wire(not taped) to the yoke describing what had transpired. After a debrief with my CFI, the aircraft was taken directly to the mechanic's shop and repaired. CFI and A&P fully agreed with my thought-process and decisions, BTW.
And did you consider this part of 91.7?
“The pilot in command shall discontinue the flight when unairworthy mechanical, electrical, or structural conditions occur.”
What was un-airworthy about the aircraft for doing VFR laps around the pattern? The powerplant was operating normally, electrical system was fine showing normal amps & volts, the airframe was still intact. The vacuum-powered gauges weren't going to implode and create a mushroom cloud. Absolutely was NOT fit for IFR flight or IMC conditions...but this was not that. Definitely not worthy of a mayday call, not even a pan-pan.
Taking a cue from QF32's Richard de Crespigny, when this failure happened I took note of what was wrong, but more importantly took note of what was still working. Everything I needed to fly safely was still working. If I had any questions, my CFI and tower were just a radio call away. I did not have any questions.
To your question if it was safe. Yes it was, but as a student pilot on you first solo, you lacked the knowledge and experience as well as the certificate required to make that determination.
A lot of assumptions in that statement because of the word "student". Student != inexperienced.
I may just be getting my PPL now, but that doesn't mean I haven't been around aviation for decades, including Part 121 and 135 operations. I was already comfortably using VORs and did my first ILS landing by my second lesson. I've done just a bit of engineering work over the years over a wide variety of industries, including automotive and aviation, in multiple continents.
There's a certain large transport-category aircraft currently in-flight which I forced a redesign of while it was still in development. I was invited to see some prototypes of the systems and a mockup of the cabin and cockpit. Me being the eternal smart-ass, found a way to inhibit some of the aircraft's systems in under 10 seconds by doing things regular passengers would normally do. Upon me demonstrating this, they were floored. They did completely redesign those systems, and reviewed other systems in the aircraft to see if they'd made similar mistakes. I'd have no problem flying on that aircraft today.
I'm not an A&P or IA, nor claim to be, nor want to be. BUT, I am a pilot, and as you're aware 91.7 also says the PIC is responsible for determining the aircraft is capable of safe flight. Not the A&P, not the IA -- the PIC is. As part of that responsibility, I'm using my past experience + learning all I can about what equipment I'm flying now...and yes, that means knowing what's underneath the cowl and seeing what's behind the panels when the plane is in annual and understanding how the rigging works.
As Wolfgang Langewiesche implores in Stick and Rudder’s first paragraph, an airplane may sound and smell like a car but it’s completely different. I ask A LOT of questions and my friends who work in ATC, A&Ps, Part 121, and NWS fortunately have a lot of patience and answer them.