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Theorem cbv3 1935
 Description: Rule used to change bound variables, using implicit substitution, that does not use ax-12o 2094. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
cbv3.1
cbv3.2
cbv3.3
Assertion
Ref Expression
cbv3

Proof of Theorem cbv3
StepHypRef Expression
1 cbv3.1 . . . 4
21a1i 10 . . 3
3 cbv3.2 . . . 4
43a1i 10 . . 3
5 cbv3.3 . . . 4
65a1i 10 . . 3
72, 4, 6cbv1 1932 . 2
8 tru 1312 . . 3
98ax-gen 1536 . 2
107, 9mpg 1538 1
 Colors of variables: wff set class Syntax hints:   wi 4   wtru 1307  wal 1530  wnf 1534 This theorem is referenced by:  cbval  1937  ax16i  1999  ax16ALT2  2001  sb8  2045  mo  2178  ax10ext  27709 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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