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Theorem bj-nnf-exlim 36758
Description: Proof of the closed form of exlimi 2216 from modalK (compare exlimiv 1929). See also bj-sylget2 36624. (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 1833 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))
2 bj-nnfe 36733 . 2 (Ⅎ'𝑥𝜓 → (∃𝑥𝜓𝜓))
31, 2syl9r 78 1 (Ⅎ'𝑥𝜓 → (∀𝑥(𝜑𝜓) → (∃𝑥𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1537  wex 1778  Ⅎ'wnnf 36725
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-bj-nnf 36726
This theorem is referenced by:  bj-19.23t  36772
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