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Theorem cbvrmov 2536
Description: Change the bound variable of a restricted uniqueness quantifier using implicit substitution. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
cbvralv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
cbvrmov  |-  ( E* x  e.  A  ph  <->  E* y  e.  A  ps )
Distinct variable groups:    x, A    y, A    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem cbvrmov
StepHypRef Expression
1 nfv 1421 . 2  |-  F/ y
ph
2 nfv 1421 . 2  |-  F/ x ps
3 cbvralv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvrmo 2532 1  |-  ( E* x  e.  A  ph  <->  E* y  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   E*wrmo 2309
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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-reu 2313  df-rmo 2314
This theorem is referenced by: (None)
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