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Theorem cbvexvw 1892
Description: Change bound variable. See cbvexv 1890 for a version with fewer disjoint variable conditions. (Contributed by NM, 19-Apr-2017.)
Hypothesis
Ref Expression
cbvalvw.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvexvw  |-  ( E. x ph  <->  E. y ps )
Distinct variable groups:    x, y    ps, x    ph, y
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvexvw
StepHypRef Expression
1 cbvalvw.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21cbvexv 1890 1  |-  ( E. x ph  <->  E. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   E.wex 1468
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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  prodmodc  11359
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