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

Theorem cbvralvw 2661
Description: Version of cbvralv 2657 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.)
Hypothesis
Ref Expression
cbvralvw.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvralvw  |-  ( A. x  e.  A  ph  <->  A. y  e.  A  ps )
Distinct variable groups:    x, y, A    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvralvw
StepHypRef Expression
1 cbvralvw.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21cbvralv 2657 1  |-  ( A. x  e.  A  ph  <->  A. y  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wral 2417
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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422
This theorem is referenced by:  cc1  7096
  Copyright terms: Public domain W3C validator