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Theorem cbvalv 1871
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 1491 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1491 . 2  |-  ( ps 
->  A. x ps )
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalh 1711 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1314
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  nfcjust  2246  cdeqal1  2873  dfss4st  3279  zfpow  4069  tfisi  4471  acexmid  5741  tfrlem3-2d  6177  tfrlemi1  6197  tfrexlem  6199  tfr1onlemaccex  6213  tfrcllemaccex  6226  findcard  6750  fisseneq  6788  genprndl  7297  genprndu  7298  zfz1iso  10552
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