Theorem 19.40 1593

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 1579	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		simpr 109	. . 3 |- ( ( ph /\ ps ) -> ps )
3	2	eximi 1562	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
4	1, 3	jca 302	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

Syntax hints:   -> wi 4   /\ wa 103   E.wex 1451

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.40-2  1594  19.41h  1646  19.41  1647  exdistrfor  1754  uniin  3722  copsexg  4126  dmin  4707  imadif  5161  imainlem  5162