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Theorem cbv2h 1728
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-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 biimp 117 . . . 4
53, 4syl6 33 . . 3
61, 2, 5cbv1h 1726 . 2
7 equcomi 1684 . . . . 5
8 biimpr 129 . . . . 5
97, 3, 8syl56 34 . . . 4
102, 1, 9cbv1h 1726 . . 3
1110a7s 1434 . 2
126, 11impbid 128 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1333 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441 This theorem is referenced by:  cbv2  1729
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