Theorem 19.40 1610

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 1596	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		simpr 109	. . 3 |- ( ( ph /\ ps ) -> ps )
3	2	eximi 1579	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
4	1, 3	jca 304	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

Syntax hints:   -> wi 4   /\ wa 103   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.40-2  1611  19.41h  1663  19.41  1664  exdistrfor  1772  uniin  3756  copsexg  4166  dmin  4747  imadif  5203  imainlem  5204