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Theorem cbval2 1957
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 22-Dec-2003.) (Revised by Mario Carneiro, 6-Oct-2016.)
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 1778 . 2
3 cbval2.3 . . 3
43nfal 1778 . 2
5 nfv 1609 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfan 1783 . . . . 5
8 nfv 1609 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfan 1783 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 424 . . . . . 6
1312pm5.32d 620 . . . . 5
147, 10, 13cbval 1937 . . . 4
15 19.28v 1848 . . . 4
16 19.28v 1848 . . . 4
1714, 15, 163bitr3i 266 . . 3
18 pm5.32 617 . . 3
1917, 18mpbir 200 . 2
202, 4, 19cbval 1937 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wnf 1534 This theorem is referenced by:  cbval2v  1959  2mo  2234  2eu6  2241 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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