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Theorem 19.39 1672
Description: Theorem 19.39 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.39  |-  ( ( E. x ph  ->  E. x ps )  ->  E. x ( ph  ->  ps ) )

Proof of Theorem 19.39
StepHypRef Expression
1 19.2 1671 . . 3  |-  ( A. x ph  ->  E. x ph )
21imim1i 54 . 2  |-  ( ( E. x ph  ->  E. x ps )  -> 
( A. x ph  ->  E. x ps )
)
3 19.35 1587 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
42, 3sylibr 203 1  |-  ( ( E. x ph  ->  E. x ps )  ->  E. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529
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