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Theorem eqvinc 3226
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 3115 . . . 4
3 ax-1 6 . . . . . 6
4 eqtr 2483 . . . . . . 7
54ex 434 . . . . . 6
63, 5jca 532 . . . . 5
76eximi 1656 . . . 4
8 pm3.43 862 . . . . 5
98eximi 1656 . . . 4
102, 7, 9mp2b 10 . . 3
111019.37iv 1769 . 2
12 eqtr2 2484 . . 3
1312exlimiv 1722 . 2
1411, 13impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109
This theorem is referenced by:  eqvincf  3227  dff13  6166  f1eqcocnv  6204  tfindsg  6695  findsg  6727  findcard2s  7781  indpi  9306  fcoinvbr  27461  dfrdg4  29600  bj-elsngl  34526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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