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Theorem 19.40 1609
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.40  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )

Proof of Theorem 19.40
StepHypRef Expression
1 exsimpl 1592 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 447 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1576 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 518 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1541
This theorem is referenced by:  19.40-2  1610  19.41  1882  19.41OLD  1883  exdistrf  1976  uniin  3928  copsexg  4334  dmin  4968  imadif  5409  fv3  5624  exan3OLD  26042  exdistrfNEW7  28928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
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