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

Theorem cbvalv 1794
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 1419 . 2  |-  ( ph  ->  A. y ph )
2 ax-17 1419 . 2  |-  ( ps 
->  A. x ps )
3 cbvalv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalh 1636 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   A.wal 1241
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-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  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:  nfcjust  2166  cdeqal1  2755  zfpow  3928  tfisi  4310  acexmid  5511  tfrlem3-2d  5928  tfrlemi1  5946  tfrexlem  5948  findcard  6345  genprndl  6619  genprndu  6620
  Copyright terms: Public domain W3C validator