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Theorem 19.39 1792
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 1759 . . 3  |-  ( A. x ph  ->  E. x ph )
21imim1i 56 . 2  |-  ( ( E. x ph  ->  E. x ps )  -> 
( A. x ph  ->  E. x ps )
)
3 19.35 1599 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
42, 3sylibr 205 1  |-  ( ( E. x ph  ->  E. x ps )  ->  E. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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