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Theorem cbv2 1980
 Description: Rule used to change bound variables, using implicit substitution. Revised to align format of hypotheses to common style. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Revised by Wolf Lammen, 13-May-2018.)
Hypotheses
Ref Expression
cbv2.1
cbv2.2
cbv2.3
cbv2.4
cbv2.5
Assertion
Ref Expression
cbv2

Proof of Theorem cbv2
StepHypRef Expression
1 cbv2.2 . . . 4
21nfri 1778 . . 3
3 cbv2.1 . . . . 5
43nfal 1864 . . . 4
54nfri 1778 . . 3
62, 5syl 16 . 2
7 cbv2.3 . . . 4
87nfrd 1779 . . 3
9 cbv2.4 . . . 4
109nfrd 1779 . . 3
11 cbv2.5 . . 3
128, 10, 11cbv2h 1979 . 2
136, 12syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wnf 1553 This theorem is referenced by:  cbvald  1986 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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