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Theorem cbv1h 1974
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-May-2018.)
Hypotheses
Ref Expression
cbv1h.1
cbv1h.2
cbv1h.3
Assertion
Ref Expression
cbv1h

Proof of Theorem cbv1h
StepHypRef Expression
1 nfa1 1806 . 2
2 nfa2 1874 . 2
3 sp 1763 . . . . 5
43sps 1770 . . . 4
5 cbv1h.1 . . . 4
64, 5syl 16 . . 3
72, 6nfd 1782 . 2
8 cbv1h.2 . . . 4
94, 8syl 16 . . 3
101, 9nfd 1782 . 2
11 cbv1h.3 . . 3
124, 11syl 16 . 2
131, 2, 7, 10, 12cbv1 1973 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549 This theorem is referenced by:  cbv3hOLD  1977  cbv2h  1979 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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