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Theorem 19.29r 1587
Description: Variation of Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
19.29r  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ph  /\  ps ) )

Proof of Theorem 19.29r
StepHypRef Expression
1 19.29 1586 . . 3  |-  ( ( A. x ps  /\  E. x ph )  ->  E. x ( ps  /\  ph ) )
21ancoms 439 . 2  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ps  /\  ph ) )
3 exancom 1576 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
42, 3sylibr 203 1  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530   E.wex 1531
This theorem is referenced by:  19.29r2  1588  19.29x  1589  exan  1835  equvini  1940  eu2  2181  intab  3908  imadif  5343  kmlem6  7797  2ndcdisj  17198  bnj907  29313  equviniNEW7  29502
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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