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Theorem 19.34 1675
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 1672 . . 3  |-  ( A. x ph  ->  E. x ph )
21orim1i 505 . 2  |-  ( ( A. x ph  \/  E. x ps )  -> 
( E. x ph  \/  E. x ps )
)
3 19.43 1593 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
42, 3sylibr 205 1  |-  ( ( A. x ph  \/  E. x ps )  ->  E. x ( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359   A.wal 1528   E.wex 1529
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-fal 1313  df-ex 1530
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