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Theorem bj-exlimmpi 11013
Description: Lemma for bj-vtoclgf 11018. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmp.nf 𝑥𝜓
bj-exlimmp.min (𝜒𝜑)
bj-exlimmpi.maj (𝜒 → (𝜑𝜓))
Assertion
Ref Expression
bj-exlimmpi (∃𝑥𝜒𝜓)

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmp.nf . 2 𝑥𝜓
2 bj-exlimmp.min . . 3 (𝜒𝜑)
3 bj-exlimmpi.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpd 13 . 2 (𝜒𝜓)
51, 4exlimi 1526 1 (∃𝑥𝜒𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1390  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-gen 1379  ax-ie2 1424  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
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