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Theorem 19.29 1596
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 pm3.2 434 . . . 4  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21alimi 1559 . . 3  |-  ( A. x ph  ->  A. x
( ps  ->  ( ph  /\  ps ) ) )
3 exim 1575 . . 3  |-  ( A. x ( ps  ->  (
ph  /\  ps )
)  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
42, 3syl 15 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
54imp 418 1  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1540   E.wex 1541
This theorem is referenced by:  19.29r  1597  19.29x  1599  equs4  1964  equvini  1992  supsrlem  8823  1stccnp  17294  iscmet3  18823  isch3  21935  stoweidlem35  27107  bnj849  28719  equviniNEW7  28948  equs4NEW7  28954
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
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