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Theorem 19.34 1674
Description: Theorem 19.34 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.34  |-  ( ( A. x ph  \/  E. x ps )  ->  E. x ( ph  \/  ps ) )

Proof of Theorem 19.34
StepHypRef Expression
1 19.2 1671 . . 3  |-  ( A. x ph  ->  E. x ph )
21orim1i 503 . 2  |-  ( ( A. x ph  \/  E. x ps )  -> 
( E. x ph  \/  E. x ps )
)
3 19.43 1592 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
42, 3sylibr 203 1  |-  ( ( A. x ph  \/  E. x ps )  ->  E. x ( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357   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-or 359  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529
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