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Theorem bj-exlimmpbir 35099
Description: Lemma for theorems of the vtoclg 3505 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 257 . 2 (𝜒𝜑)
51, 4exlimi 2210 1 (∃𝑥𝜒𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wex 1782  wnf 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-ex 1783  df-nf 1787
This theorem is referenced by: (None)
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