PA-28 PLT HAD AN EXCURSION FROM ASSIGNED ALT THAT LEADS TO A DSCNT BELOW MSA IN THE PHOENIX AREA ON AN IFR NIGHT TRAINING FLT.

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MY INSTRUCTOR AND I WERE ON A XCOUNTRY IFR FLT. WE WERE BEING VECTORED TO OUR FINAL DEST; DEER VALLEY ARPT IN PHOENIX. WE WERE TOLD TO DSND TO 6000 FT AND I HEARD 4000 FT MISTAKENLY. AFTER DSNDING TO 5000 FT; MY INSTRUCTOR SAID DO NOT DSND ANYMORE. AT THAT POINT MY INSTRUCTOR TOLD ME TO CLB AND ATC SAID THE SAME THING. WE WERE TOLD TO CALL THE TWR WHEN WE LANDED. IT WAS XA00 WHEN THE INCIDENT OCCURRED OVER WHITE TANK MOUNTAINS. FATIGUE WAS A CONTRIBUTING FACTOR. MY INSTRUCTOR HAD A VISUAL OF THE MOUNTAIN TOP AND THAT'S HOW IT WAS DISCOVERED WE WERE TOO LOW. FROM THERE; A CLB WAS INITIATED. SUPPLEMENTAL INFO FROM ACN #567069: MY STUDENT AND I WERE ON A 250 NM NIGHT IFR XCOUNTRY TO SATISFY TRAINING REQUIREMENTS. WE REQUESTED THE GPS RWY 7R APCH INTO DVT. AFTER XING THE BXK VOR; ABOUT 2 NM AFTER; WE WERE VECTORED OFF OF V-16 TO FLY DIRECT TO BOLES INTXN ON THE APCH. WE WERE ALSO TOLD TO DSND FROM 7000 FT TO 6000 FT. I WAS QUIZZING MY STUDENT ON SEVERAL DIFFERENT ASPECTS CONCERNING THE APCH; AND EVENTUALLY ASKED HIM WHAT ALT WE HAD BEEN CLRED TO. HE SAID 4000 FT. THINKING THAT I HAD MISSED THAT INSTRUCTION FROM ATC AND THINKING THAT IT SEEMED LIKE AN APPROPRIATE STEP DOWN ALT; I BELIEVED HIM. I WAS MAINTAINING VISUAL WITH THE WHITE TANK MOUNTAINS; AND UPON REACHING 5000 FT; I TOLD HIM TO LOOK OUTSIDE AND STOP THE DSCNT IMMEDIATELY. THE MOUNTAINS SEEMED CLOSER THAN WHAT ATC WOULD VECTOR US FOR. ATC THEN CALLED AND TOLD US TO CLB IMMEDIATELY; WHICH WE DID BACK TO 6000 FT. CONTRIBUTING FACTOR MAY HAVE BEEN NIGHT FATIGUE AND INSTRUCTOR'S FAILURE TO VERIFY ASSIGNED ALT.