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Theorem cbv2OLD 1979
Description: Obsolete version of cbv2 1978 as of 31-Dec-2018. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cbv2OLD.1  |-  ( ph  ->  F/ y ps )
cbv2OLD.2  |-  ( ph  ->  F/ x ch )
cbv2OLD.3  |-  ( ph  ->  ( x  =  y  ->  ( ps  <->  ch )
) )
Assertion
Ref Expression
cbv2OLD  |-  ( A. x A. y ph  ->  ( A. x ps  <->  A. y ch ) )

Proof of Theorem cbv2OLD
StepHypRef Expression
1 cbv2OLD.1 . . 3  |-  ( ph  ->  F/ y ps )
21nfrd 1813 . 2  |-  ( ph  ->  ( ps  ->  A. y ps ) )
3 cbv2OLD.2 . . 3  |-  ( ph  ->  F/ x ch )
43nfrd 1813 . 2  |-  ( ph  ->  ( ch  ->  A. x ch ) )
5 cbv2OLD.3 . 2  |-  ( ph  ->  ( x  =  y  ->  ( ps  <->  ch )
) )
62, 4, 5cbv2h 1977 1  |-  ( A. x A. y ph  ->  ( A. x ps  <->  A. y ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368   F/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 1954
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by: (None)
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