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Theorem eqvinc 3055
 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 2954 . . . 4
3 ax-1 5 . . . . . 6
4 eqtr 2452 . . . . . . 7
54ex 424 . . . . . 6
63, 5jca 519 . . . . 5
76eximi 1585 . . . 4
8 pm3.43 833 . . . . 5
98eximi 1585 . . . 4
102, 7, 9mp2b 10 . . 3
111019.37aiv 1923 . 2
12 eqtr2 2453 . . 3
1312exlimiv 1644 . 2
1411, 13impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cvv 2948 This theorem is referenced by:  eqvincf  3056  tfindsg  4832  findsg  4864  dff13  5996  f1eqcocnv  6020  findcard2s  7341  indpi  8774  dfrdg4  25760 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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