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Theorem bj-exlimmpi 12966
Description: Lemma for bj-vtoclgf 12972. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmp.nf  |-  F/ x ps
bj-exlimmp.min  |-  ( ch 
->  ph )
bj-exlimmpi.maj  |-  ( ch 
->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-exlimmpi  |-  ( E. x ch  ->  ps )

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmp.nf . 2  |-  F/ x ps
2 bj-exlimmp.min . . 3  |-  ( ch 
->  ph )
3 bj-exlimmpi.maj . . 3  |-  ( ch 
->  ( ph  ->  ps ) )
42, 3mpd 13 . 2  |-  ( ch 
->  ps )
51, 4exlimi 1573 1  |-  ( E. x ch  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1436   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1425  ax-ie2 1470  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by: (None)
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