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Theorem cbval2 1891
 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
cbval2.2
cbval2.3
cbval2.4
cbval2.5
Assertion
Ref Expression
cbval2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbval2
StepHypRef Expression
1 cbval2.1 . . 3
21nfal 1555 . 2
3 cbval2.3 . . 3
43nfal 1555 . 2
5 nfv 1508 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfim 1551 . . . . 5
8 nfv 1508 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfim 1551 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 115 . . . . . 6
1312pm5.74d 181 . . . . 5
147, 10, 13cbval 1727 . . . 4
15 19.21v 1845 . . . 4
16 19.21v 1845 . . . 4
1714, 15, 163bitr3i 209 . . 3
1817pm5.74ri 180 . 2
192, 4, 18cbval 1727 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329  wnf 1436 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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  cbval2v  1893
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