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Theorem 19.34 1574
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 1529 . . 3  |-  ( A. x ph  ->  E. x ph )
21orim1i 677 . 2  |-  ( ( A. x ph  \/  E. x ps )  -> 
( E. x ph  \/  E. x ps )
)
3 19.43 1519 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
42, 3sylibr 137 1  |-  ( ( A. x ph  \/  E. x ps )  ->  E. x ( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 629   A.wal 1241   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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