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Theorem bj-nnf-exlim 34085
Description: Proof of the closed form of exlimi 2213 from modalK (compare exlimiv 1927). See also bj-sylget2 33955. (Contributed by BJ, 2-Dec-2023.)
Assertion
Ref Expression
bj-nnf-exlim (Ⅎ'𝑥𝜓 → (∀𝑥(𝜑𝜓) → (∃𝑥𝜑𝜓)))

Proof of Theorem bj-nnf-exlim
StepHypRef Expression
1 exim 1830 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))
2 bj-nnfe 34062 . 2 (Ⅎ'𝑥𝜓 → (∃𝑥𝜓𝜓))
31, 2syl9r 78 1 (Ⅎ'𝑥𝜓 → (∀𝑥(𝜑𝜓) → (∃𝑥𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1776  Ⅎ'wnnf 34055
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-bj-nnf 34056
This theorem is referenced by:  bj-19.23t  34099
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