Theorem exan3OLD 26592

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 1616	. 2 |- ( E. x ( ph /\ ps ) -> ( E. x ph /\ E. x ps ) )
2	1	simprd 450	1 |- ( E. x ( ph /\ ps ) -> E. x ps )

Syntax hints:   -> wi 4   /\ wa 359   E.wex 1547

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563

This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548