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Theorem cbvalv 1810
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 1435 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1435 . 2  |-  ( ps 
->  A. x ps )
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalh 1652 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 102   A.wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfcjust  2182  cdeqal1  2778  zfpow  3956  tfisi  4338  acexmid  5539  tfrlem3-2d  5959  tfrlemi1  5977  tfrexlem  5979  findcard  6376  genprndl  6677  genprndu  6678
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