Theorem 19.40 1563

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 1549	. 2 |- ( E. x ( ph /\ ps ) -> E. x ph )
2		simpr 108	. . 3 |- ( ( ph /\ ps ) -> ps )
3	2	eximi 1532	. 2 |- ( E. x ( ph /\ ps ) -> E. x ps )
4	1, 3	jca 300	1 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )

Syntax hints:   -> wi 4   /\ wa 102   E.wex 1422

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  19.40-2  1564  19.41h  1616  19.41  1617  exdistrfor  1723  uniin  3641  copsexg  4027  dmin  4591  imadif  5030  imainlem  5031