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Theorem 19.23v 1805
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 1460 . 2  |-  ( ps 
->  A. x ps )
2119.23h 1428 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   E.wex 1422
This theorem was proved from axioms:  ax-mp 7  ax-gen 1379  ax-ie2 1424  ax-17 1460
This theorem is referenced by:  19.23vv  1806  2eu4  2035  gencbval  2648  euind  2780  reuind  2796  unissb  3639  dftr2  3885  ssrelrel  4466  cotr  4736  dffun2  4942  fununi  4998  dff13  5439  acexmidlem2  5540
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