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Theorem cbval2 1793
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 22-Dec-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 22-Apr-2018.)
Hypotheses
Ref Expression
cbval2.1  F/
cbval2.2  F/
cbval2.3  F/
cbval2.4  F/
cbval2.5
Assertion
Ref Expression
cbval2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbval2
StepHypRef Expression
1 cbval2.1 . . 3  F/
21nfal 1465 . 2  F/
3 cbval2.3 . . 3  F/
43nfal 1465 . 2  F/
5 nfv 1418 . . . . . 6  F/
6 cbval2.2 . . . . . 6  F/
75, 6nfim 1461 . . . . 5  F/
8 nfv 1418 . . . . . 6  F/
9 cbval2.4 . . . . . 6  F/
108, 9nfim 1461 . . . . 5  F/
11 cbval2.5 . . . . . . 7
1211expcom 109 . . . . . 6
1312pm5.74d 171 . . . . 5
147, 10, 13cbval 1634 . . . 4
15 19.21v 1750 . . . 4
16 19.21v 1750 . . . 4
1714, 15, 163bitr3i 199 . . 3
1817pm5.74ri 170 . 2
192, 4, 18cbval 1634 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   F/wnf 1346
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  cbval2v  1795
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