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Theorem 19.29r 1596
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 1595 . . 3  |-  ( ( A. x ps  /\  E. x ph )  ->  E. x ( ps  /\  ph ) )
21ancoms 441 . 2  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ps  /\  ph ) )
3 exancom 1584 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
42, 3sylibr 205 1  |-  ( ( E. x ph  /\  A. 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:  19.29r2  1597  19.29x  1598  exan  1807  equvini  1879  eu2  2138  intab  3790  imadif  5184  kmlem6  7665  2ndcdisj  17014  bnj907  27686
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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