Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  qseq1 Structured version   Unicode version

Theorem qseq1 7373
 Description: Equality theorem for quotient set. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
qseq1

Proof of Theorem qseq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexeq 3064 . . 3
21abbidv 2603 . 2
3 df-qs 7329 . 2
4 df-qs 7329 . 2
52, 3, 43eqtr4g 2533 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379  cab 2452  wrex 2818  cec 7321  cqs 7322 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2823  df-qs 7329 This theorem is referenced by:  pi1bas  21404  pstmval  27706
 Copyright terms: Public domain W3C validator