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Theorem exan3OLD 26719
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 1596 . 2  |-  ( E. x ( ph  /\  ps )  ->  ( E. x ph  /\  E. x ps ) )
21simprd 449 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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