ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  chvarv Unicode version

Theorem chvarv 1812
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 1740 . 2  |-  ( A. x ph  ->  ps )
3 chv.2 . 2  |-  ph
42, 3mpg 1340 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  axext3  2023  axsep2  3876  tz6.12f  5202  tfrlem3-2  5927  bdsep2  10006  strcoll2  10108
  Copyright terms: Public domain W3C validator