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Theorem 19.40 1620
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 1603 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 449 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1586 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 520 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   E.wex 1551
This theorem is referenced by:  19.40-2  1621  19.41  1901  19.41OLD  1902  exdistrf  2067  exdistrfOLD  2068  uniin  4037  copsexg  4444  dmin  5079  imadif  5530  fv3  5746  exan3OLD  26704  exdistrfNEW7  29567
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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