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Theorem 19.29r 1601
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 1600 . 2  |-  ( ( A. x ps  /\  E. x ph )  ->  E. x ( ps  /\  ph ) )
2 ancom 264 . 2  |-  ( ( E. x ph  /\  A. x ps )  <->  ( A. x ps  /\  E. x ph ) )
3 exancom 1588 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
41, 2, 33imtr4i 200 1  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1330   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.29r2  1602  19.29x  1603  exan  1672  ax9o  1677  equvini  1732  eu2  2044  intab  3807  imadiflem  5209  bj-inex  13274
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