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Theorem 19.40 1647
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 26-May-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 1645 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 exsimpr 1646 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
31, 2jca 532 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by:  19.40-2  1665  19.41  1911  exdistrf  2035  uniin  4220  copsexg  4685  copsexgOLD  4686  dmin  5156  imadif  5602  bj-19.40b  32495
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