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Theorem r19.3rmv 3339
Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 6-Aug-2018.)
Assertion
Ref Expression
r19.3rmv  |-  ( E. y  y  e.  A  ->  ( ph  <->  A. x  e.  A  ph ) )
Distinct variable groups:    x, A    y, A    ph, x
Allowed substitution hint:    ph( y)

Proof of Theorem r19.3rmv
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
21r19.3rm 3337 1  |-  ( E. y  y  e.  A  ->  ( ph  <->  A. x  e.  A  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   E.wex 1422    e. wcel 1434   A.wral 2349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-cleq 2075  df-clel 2078  df-ral 2354
This theorem is referenced by:  iinconstm  3695  cnvpom  4890  ssfilem  6410  diffitest  6421  caucvgsrlemasr  7028  resqrexlemgt0  10044
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