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Theorem cbv2 1635
 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 1412 . . 3
3 cbv2.1 . . . . 5
43nfal 1468 . . . 4
54nfri 1412 . . 3
62, 5syl 14 . 2
7 cbv2.3 . . . 4
87nfrd 1413 . . 3
9 cbv2.4 . . . 4
109nfrd 1413 . . 3
11 cbv2.5 . . 3
128, 10, 11cbv2h 1634 . 2
136, 12syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241  wnf 1349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  cbvald  1800  cbvrald  9927
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