ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cbval2vw Unicode version

Theorem cbval2vw 1944
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 4-Feb-2005.) (Revised by GG, 10-Jan-2024.)
Hypothesis
Ref Expression
cbval2vw.1  |-  ( ( x  =  z  /\  y  =  w )  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
cbval2vw  |-  ( A. x A. y ph  <->  A. z A. w ps )
Distinct variable groups:    z, w, ph    x, y, ps    x, w, y, z
Allowed substitution hints:    ph( x, y)    ps( z, w)

Proof of Theorem cbval2vw
StepHypRef Expression
1 cbval2vw.1 . . 3  |-  ( ( x  =  z  /\  y  =  w )  ->  ( ph  <->  ps )
)
21cbvaldvaw 1942 . 2  |-  ( x  =  z  ->  ( A. y ph  <->  A. w ps ) )
32cbvalvw 1931 1  |-  ( A. x A. y ph  <->  A. z A. w ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105   A.wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-nf 1472
This theorem is referenced by:  seqf1og  10582
  Copyright terms: Public domain W3C validator