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Theorem 19.29 1595
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 1546 . . 3  |-  ( A. x ph  ->  A. x
( ps  ->  ( ph  /\  ps ) ) )
3 exim 1573 . . 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 1532   E.wex 1537
This theorem is referenced by:  19.29r  1596  19.29x  1598  equs4  1849  equvini  1879  supsrlem  8613  1stccnp  17020  iscmet3  18551  isch3  21651  bnj849  27646
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
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