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Theorem cbv2h 2019
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 11-May-1993.)
Hypotheses
Ref Expression
cbv2h.1
cbv2h.2
cbv2h.3
Assertion
Ref Expression
cbv2h

Proof of Theorem cbv2h
StepHypRef Expression
1 cbv2h.1 . . 3
2 cbv2h.2 . . 3
3 cbv2h.3 . . . 4
4 bi1 186 . . . 4
53, 4syl6 33 . . 3
61, 2, 5cbv1h 2018 . 2
7 equcomi 1793 . . . . 5
8 bi2 198 . . . . 5
97, 3, 8syl56 34 . . . 4
102, 1, 9cbv1h 2018 . . 3
1110alcoms 1843 . 2
126, 11impbid 191 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393 This theorem is referenced by:  cbv2  2020  eujustALT  2285 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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