Theorem 19.40 1679

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

Step	Hyp	Ref	Expression
1		exsimpl 1665	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		simpr 110	. . 3 |- ( ( ph /\ ps ) -> ps )
3	2	eximi 1648	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
4	1, 3	jca 306	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-ial 1582

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.40-2  1680  19.41h  1733  19.41  1734  exdistrfor  1848  uniin  3913  copsexg  4336  dmin  4939  imadif  5410  imainlem  5411