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Theorem eqvinc 3212
 Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
eqvinc.1
Assertion
Ref Expression
eqvinc
Distinct variable groups:   ,   ,

Proof of Theorem eqvinc
StepHypRef Expression
1 eqvinc.1 . . . . 5
21isseti 3101 . . . 4
3 ax-1 6 . . . . . 6
4 eqtr 2469 . . . . . . 7
54ex 434 . . . . . 6
63, 5jca 532 . . . . 5
76eximi 1643 . . . 4
8 pm3.43 862 . . . . 5
98eximi 1643 . . . 4
102, 7, 9mp2b 10 . . 3
111019.37aiv 1756 . 2
12 eqtr2 2470 . . 3
1312exlimiv 1709 . 2
1411, 13impbii 188 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1383  wex 1599   wcel 1804  cvv 3095 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-12 1840  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-v 3097 This theorem is referenced by:  eqvincf  3213  dff13  6151  f1eqcocnv  6189  tfindsg  6680  findsg  6712  findcard2s  7763  indpi  9288  fcoinvbr  27439  dfrdg4  29576  bj-elsngl  34409
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