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Theorem 19.29 1584
Description: Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
19.29  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )

Proof of Theorem 19.29
StepHypRef Expression
1 pm3.2 436 . . . 4  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21alimi 1547 . . 3  |-  ( A. x ph  ->  A. x
( ps  ->  ( ph  /\  ps ) ) )
3 exim 1563 . . 3  |-  ( A. x ( ps  ->  (
ph  /\  ps )
)  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
42, 3syl 17 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
54imp 420 1  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360   A.wal 1528   E.wex 1529
This theorem is referenced by:  19.29r  1585  19.29x  1587  equs4  1901  equvini  1929  supsrlem  8728  1stccnp  17182  iscmet3  18713  isch3  21813  stoweidlem35  27183  bnj849  28224
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530
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