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Theorem 19.23h 1993
Description: Theorem 19.23 of [Margaris] p. 90. See 19.23 1992. (Contributed by NM, 24-Jan-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 1673 . 2  |-  F/ x ps
3219.23 1992 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   A.wal 1441   E.wex 1662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667
This theorem is referenced by:  equsalhw  2027
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