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Theorem 19.23v 1811
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 1464 . 2  |-  ( ps 
->  A. x ps )
2119.23h 1432 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-mp 7  ax-gen 1383  ax-ie2 1428  ax-17 1464
This theorem is referenced by:  19.23vv  1812  2eu4  2041  gencbval  2667  euind  2802  reuind  2820  unissb  3683  disjnim  3836  dftr2  3938  ssrelrel  4538  cotr  4813  dffun2  5025  fununi  5082  dff13  5547  acexmidlem2  5649
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