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Theorem cbvalv 1839
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 1462 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1462 . 2  |-  ( ps 
->  A. x ps )
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalh 1680 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  nfcjust  2213  cdeqal1  2820  dfss4st  3221  zfpow  3987  tfisi  4377  acexmid  5614  tfrlem3-2d  6033  tfrlemi1  6053  tfrexlem  6055  tfr1onlemaccex  6069  tfrcllemaccex  6082  findcard  6558  fisseneq  6595  genprndl  7027  genprndu  7028  zfz1iso  10164
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