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Theorem 19.40 1601
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 1584 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 449 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1568 . 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 6    /\ wa 360   E.wex 1533
This theorem is referenced by:  19.40-2  1602  19.41  1819  exdistrf  1914  uniin  3848  copsexg  4251  dmin  4885  imadif  5292  fv3  5501  exan3OLD  26118
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1534
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