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Theorem 19.29 1651
Description: Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 21-Jun-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 pm3.2 447 . . 3  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21aleximi 1623 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
32imp 429 1  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by:  19.29r  1652  19.29x  1654  supsrlem  9390  1stccnp  19199  iscmet3  20937  tgldim0eq  23092  isch3  24797  stoweidlem35  29979  bnj849  32251  bj-19.40b  32495
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