Theorem exan3OLD 26716

Description: Cancel a conjunct from the scope of an existential quantifier. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
exan3OLD	|- ( E. x ( ph /\ ps ) -> E. x ps )

Proof of Theorem exan3OLD

Step	Hyp	Ref	Expression
1		19.40 1620	. 2 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )
2	1	simprd 451	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 360   E.wex 1551

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567

This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552