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Theorem 19.19 1791
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 1785 . 2  |-  ( E. x ph  <->  ph )
3 exbi 1570 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
42, 3syl5bbr 250 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1529   E.wex 1530   F/wnf 1533
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-ex 1531  df-nf 1534
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