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Theorem bj-exlimmpi 31512
Description: Lemma for bj-vtoclg1f1 31517 (an instance of this lemma is a version of bj-vtoclg1f1 31517 where  x and  y are identified). (Contributed by BJ, 30-Apr-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpi.nf  |-  F/ x ps
bj-exlimmpi.maj  |-  ( ch 
->  ( ph  ->  ps ) )
bj-exlimmpi.min  |-  ph
Assertion
Ref Expression
bj-exlimmpi  |-  ( E. x ch  ->  ps )

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmpi.nf . 2  |-  F/ x ps
2 bj-exlimmpi.min . . 3  |-  ph
3 bj-exlimmpi.maj . . 3  |-  ( ch 
->  ( ph  ->  ps ) )
42, 3mpi 20 . 2  |-  ( ch 
->  ps )
51, 4exlimi 1995 1  |-  ( E. x ch  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1663   F/wnf 1667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668
This theorem is referenced by:  bj-vtoclg1f1  31517  bj-vtoclg1f  31518  bj-vtoclg1fv  31519
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