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Theorem 19.40 1624
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 1610 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 simpr 109 . . 3  |-  ( (
ph  /\  ps )  ->  ps )
32eximi 1593 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
41, 3jca 304 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   E.wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.40-2  1625  19.41h  1678  19.41  1679  exdistrfor  1793  uniin  3816  copsexg  4229  dmin  4819  imadif  5278  imainlem  5279
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