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Theorem 19.29 1556
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 pm3.2 137 . . . 4  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21alimi 1389 . . 3  |-  ( A. x ph  ->  A. x
( ps  ->  ( ph  /\  ps ) ) )
3 exim 1535 . . 3  |-  ( A. x ( ps  ->  (
ph  /\  ps )
)  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
42, 3syl 14 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x
( ph  /\  ps )
) )
54imp 122 1  |-  ( ( A. x ph  /\  E. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.29r  1557  19.29x  1559  19.35-1  1560  equs4  1660  equvini  1688  rexxfrd  4276  funimaexglem  5083  bj-inex  11444
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