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Theorem 19.19 1881
Description: Theorem 19.19 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.19.1  |-  F/ x ph
Assertion
Ref Expression
19.19  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )

Proof of Theorem 19.19
StepHypRef Expression
1 19.19.1 . . 3  |-  F/ x ph
2119.9 1793 . 2  |-  ( E. x ph  <->  ph )
3 exbi 1588 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
42, 3syl5bbr 251 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546   E.wex 1547   F/wnf 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551
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