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Theorem cbv3 1968
 Description: Rule used to change bound variables, using implicit substitution, that does not use ax-c9 2199. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-May-2018.)
Hypotheses
Ref Expression
cbv3.1
cbv3.2
cbv3.3
Assertion
Ref Expression
cbv3

Proof of Theorem cbv3
StepHypRef Expression
1 cbv3.1 . . 3
21nfal 1882 . 2
3 cbv3.2 . . 3
4 cbv3.3 . . 3
53, 4spim 1959 . 2
62, 5alrimi 1813 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1368  wnf 1590 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591 This theorem is referenced by:  cbv3h  1969  cbv1  1970  cbval  1978  axc16i  2021  mo3OLD  2306  moOLD  2312  axc11next  29800
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