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Theorem bj-exlimmpbi 31897
Description: Lemma for theorems of the vtoclg 3234 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpbi.nf 𝑥𝜓
bj-exlimmpbi.maj (𝜒 → (𝜑𝜓))
bj-exlimmpbi.min 𝜑
Assertion
Ref Expression
bj-exlimmpbi (∃𝑥𝜒𝜓)

Proof of Theorem bj-exlimmpbi
StepHypRef Expression
1 bj-exlimmpbi.nf . 2 𝑥𝜓
2 bj-exlimmpbi.min . . 3 𝜑
3 bj-exlimmpbi.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpbii 221 . 2 (𝜒𝜓)
51, 4exlimi 2070 1 (∃𝑥𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wex 1694  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-12 2031
This theorem depends on definitions:  df-bi 195  df-or 383  df-ex 1695  df-nf 1700
This theorem is referenced by: (None)
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