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Theorem 19.29r 1553
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 1552 . 2  |-  ( ( A. x ps  /\  E. x ph )  ->  E. x ( ps  /\  ph ) )
2 ancom 262 . 2  |-  ( ( E. x ph  /\  A. x ps )  <->  ( A. x ps  /\  E. x ph ) )
3 exancom 1540 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
41, 2, 33imtr4i 199 1  |-  ( ( E. x ph  /\  A. x ps )  ->  E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1283   E.wex 1422
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.29r2  1554  19.29x  1555  exan  1624  ax9o  1629  equvini  1682  eu2  1986  intab  3673  imadiflem  5009  bj-inex  10856
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