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Theorem 19.24 1677
Description: Theorem 19.24 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.24  |-  ( ( A. x ph  ->  A. x ps )  ->  E. x ( ph  ->  ps ) )

Proof of Theorem 19.24
StepHypRef Expression
1 19.2 1675 . . 3  |-  ( A. x ps  ->  E. x ps )
21imim2i 15 . 2  |-  ( ( A. x ph  ->  A. x ps )  -> 
( A. x ph  ->  E. x ps )
)
3 19.35 1592 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
42, 3sylibr 205 1  |-  ( ( A. x ph  ->  A. x ps )  ->  E. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1533
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-fal 1316  df-ex 1534
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