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Theorem bj-exlime 30999
Description: Variant of exlimih 1971 where the non-freeness of  x in  ps is expressed using an existential quantifier. (Contributed by BJ, 17-Mar-2020.)
Hypotheses
Ref Expression
bj-exlime.1  |-  ( E. x ps  ->  ps )
bj-exlime.2  |-  ( ph  ->  ps )
Assertion
Ref Expression
bj-exlime  |-  ( E. x ph  ->  ps )

Proof of Theorem bj-exlime
StepHypRef Expression
1 bj-exlime.2 . . 3  |-  ( ph  ->  ps )
21eximi 1703 . 2  |-  ( E. x ph  ->  E. x ps )
3 bj-exlime.1 . 2  |-  ( E. x ps  ->  ps )
42, 3syl 17 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  bj-cbvexiw  31012
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