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Theorem eqvinc 2895
 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 2794 . . . 4
3 ax-1 5 . . . . . 6
4 eqtr 2300 . . . . . . 7
54ex 423 . . . . . 6
63, 5jca 518 . . . . 5
76eximi 1563 . . . 4
8 pm3.43 832 . . . . 5
98eximi 1563 . . . 4
102, 7, 9mp2b 9 . . 3
111019.37aiv 1841 . 2
12 eqtr2 2301 . . 3
1312exlimiv 1666 . 2
1411, 13impbii 180 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1528   wceq 1623   wcel 1684  cvv 2788 This theorem is referenced by:  eqvincf  2896  tfindsg  4651  findsg  4683  dff13  5783  f1eqcocnv  5805  findcard2s  7099  indpi  8531  dfrdg4  24488 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-v 2790
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