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Theorem 19.19 1769
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 1762 . 2  |-  ( E. x ph  <->  ph )
3 exbi 1579 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
42, 3syl5bbr 252 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E.wex 1537   F/wnf 1539
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-ex 1538  df-nf 1540
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