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Theorem 19.23h 1822
Description: Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypothesis
Ref Expression
19.23h.1  |-  ( ps 
->  A. x ps )
Assertion
Ref Expression
19.23h  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )

Proof of Theorem 19.23h
StepHypRef Expression
1 19.23h.1 . . 3  |-  ( ps 
->  A. x ps )
21nfi 1561 . 2  |-  F/ x ps
3219.23 1821 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   A.wal 1550   E.wex 1551
This theorem is referenced by:  exlimihOLD  1825  equsalhw  1862
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-11 1763
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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