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Theorem 19.40 1631
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 1617 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 110 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1600 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 306 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  19.40-2  1632  19.41h  1685  19.41  1686  exdistrfor  1800  uniin  3829  copsexg  4243  dmin  4834  imadif  5295  imainlem  5296
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