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

Step	Hyp	Ref	Expression
1		exsimpl 1645	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		exsimpr 1646	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
3	1, 2	jca 532	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

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