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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
StepHypRef Expression
1 19.40 1620 . 2  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
21simprd 451 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff set class
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
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