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Theorem eqvincg 2668
 Description: A variable introduction law for class equality, deduction version. (Contributed by Thierry Arnoux, 2-Mar-2017.)
Assertion
Ref Expression
eqvincg
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eqvincg
StepHypRef Expression
1 elisset 2568 . . . 4
2 ax-1 5 . . . . . 6
3 eqtr 2057 . . . . . . 7
43ex 108 . . . . . 6
52, 4jca 290 . . . . 5
65eximi 1491 . . . 4
7 pm3.43 534 . . . . 5
87eximi 1491 . . . 4
91, 6, 83syl 17 . . 3
10 nfv 1421 . . . 4
111019.37-1 1564 . . 3
129, 11syl 14 . 2
13 eqtr2 2058 . . 3
1413exlimiv 1489 . 2
1512, 14impbid1 130 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wex 1381   wcel 1393 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by:  dff13  5407  f1eqcocnv  5431
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