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

Step	Hyp	Ref	Expression
1		exsimpl 1729	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		exsimpr 1730	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
3	1, 2	jca 535	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

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