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Theorem 19.40 1731
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 1729 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
2 exsimpr 1730 . 2  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
31, 2jca 535 1  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371   E.wex 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664
This theorem is referenced by:  19.40-2  1749  19.40b  1750  19.40bOLD  1751  19.41v  1830  19.41  2051  exdistrf  2167  uniin  4218  copsexg  4687  dmin  5042  imadif  5658  bj-19.41al  31250
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