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Theorem 19.40 1619
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 1602 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 448 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1585 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 519 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   E.wex 1550
This theorem is referenced by:  19.40-2  1620  19.41  1900  19.41OLD  1901  exdistrf  2066  exdistrfOLD  2067  uniin  4035  copsexg  4442  dmin  5077  imadif  5528  fv3  5744  exan3OLD  26702  exdistrfNEW7  29505
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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