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Theorem 19.23v 1837
Description: Special case of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
19.23v  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem 19.23v
StepHypRef Expression
1 ax-17 1489 . 2  |-  ( ps 
->  A. x ps )
2119.23h 1457 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   E.wex 1451
This theorem was proved from axioms:  ax-mp 5  ax-gen 1408  ax-ie2 1453  ax-17 1489
This theorem is referenced by:  19.23vv  1838  2eu4  2068  gencbval  2706  euind  2842  reuind  2860  unissb  3734  disjnim  3888  dftr2  3996  ssrelrel  4607  cotr  4888  dffun2  5101  fununi  5159  dff13  5635  acexmidlem2  5737
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