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Theorem chvarv 1854
Description: Implicit substitution of  y for  x into a theorem. (Contributed by NM, 20-Apr-1994.)
Hypotheses
Ref Expression
chv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
chv.2  |-  ph
Assertion
Ref Expression
chvarv  |-  ps
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem chvarv
StepHypRef Expression
1 chv.1 . . 3  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21spv 1782 . 2  |-  ( A. x ph  ->  ps )
3 chv.2 . 2  |-  ph
42, 3mpg 1381 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  axext3  2065  axsep2  3899  tz6.12f  5228  bdsep2  10820  strcoll2  10921
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