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Theorem cbvalv 1869
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
cbvalv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvalv  |-  ( A. x ph  <->  A. y ps )
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvalv
StepHypRef Expression
1 ax-17 1489 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1489 . 2  |-  ( ps 
->  A. x ps )
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalh 1709 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312
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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  nfcjust  2244  cdeqal1  2871  dfss4st  3277  zfpow  4067  tfisi  4469  acexmid  5739  tfrlem3-2d  6175  tfrlemi1  6195  tfrexlem  6197  tfr1onlemaccex  6211  tfrcllemaccex  6224  findcard  6748  fisseneq  6786  genprndl  7293  genprndu  7294  zfz1iso  10524
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