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Theorem chvarv 1917
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 1840 . 2  |-  ( A. x ph  ->  ps )
3 chv.2 . 2  |-  ph
42, 3mpg 1431 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1441
This theorem is referenced by:  axext3  2140  axsep2  4083  tz6.12f  5497  ltordlem  8357  bdsep2  13461  strcoll2  13558
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