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Theorem eqvinc 2661
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  _V
Assertion
Ref Expression
eqvinc
Distinct variable groups:   ,   ,

Proof of Theorem eqvinc
StepHypRef Expression
1 eqvinc.1 . . . . 5  _V
21isseti 2557 . . . 4
3 ax-1 5 . . . . . 6
4 eqtr 2054 . . . . . . 7
54ex 108 . . . . . 6
63, 5jca 290 . . . . 5
76eximi 1488 . . . 4
8 pm3.43 534 . . . . 5
98eximi 1488 . . . 4
102, 7, 9mp2b 8 . . 3
111019.37aiv 1562 . 2
12 eqtr2 2055 . . 3
1312exlimiv 1486 . 2
1411, 13impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242  wex 1378   wcel 1390   _Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  eqvincf  2663
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