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Theorem eqvincg 28091
 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 3092 . . . 4
2 ax-1 6 . . . . . 6
3 eqtr 2448 . . . . . . 7
43ex 435 . . . . . 6
52, 4jca 534 . . . . 5
65eximi 1702 . . . 4
7 pm3.43 870 . . . . 5
87eximi 1702 . . . 4
91, 6, 83syl 18 . . 3
10 19.37v 1815 . . 3
119, 10sylib 199 . 2
12 eqtr2 2449 . . 3
1312exlimiv 1766 . 2
1411, 13impbid1 206 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1659   wcel 1868 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-12 1905  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3083 This theorem is referenced by:  funcnv5mpt  28259
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