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Theorem qsinxp 7405
 Description: Restrict the equivalence relation in a quotient set to the base set. (Contributed by Mario Carneiro, 23-Feb-2015.)
Assertion
Ref Expression
qsinxp

Proof of Theorem qsinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ecinxp 7404 . . . . 5
21eqeq2d 2471 . . . 4
32rexbidva 2965 . . 3
43abbidv 2593 . 2
5 df-qs 7335 . 2
6 df-qs 7335 . 2
74, 5, 63eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  cab 2442  wrex 2808   cin 3470   wss 3471   cxp 5006  cima 5011  cec 7327  cqs 7328 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457  df-opab 4516  df-xp 5014  df-rel 5015  df-cnv 5016  df-dm 5018  df-rn 5019  df-res 5020  df-ima 5021  df-ec 7331  df-qs 7335 This theorem is referenced by:  pi1buni  21666  pi1bas3  21669
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