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Theorem bj-exlimmpbir 32099
 Description: Lemma for theorems of the vtoclg 3239 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpbir.nf 𝑥𝜑
bj-exlimmpbir.maj (𝜒 → (𝜑𝜓))
bj-exlimmpbir.min 𝜓
Assertion
Ref Expression
bj-exlimmpbir (∃𝑥𝜒𝜑)

Proof of Theorem bj-exlimmpbir
StepHypRef Expression
1 bj-exlimmpbir.nf . 2 𝑥𝜑
2 bj-exlimmpbir.min . . 3 𝜓
3 bj-exlimmpbir.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpbiri 247 . 2 (𝜒𝜑)
51, 4exlimi 2073 1 (∃𝑥𝜒𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∃wex 1695  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701 This theorem is referenced by: (None)
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