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Theorem bj-nnf-alrim 35937
Description: Proof of the closed form of alrimi 2205 from modalK (compare alrimiv 1929). See also bj-alrim 35875. Actually, most proofs between 19.3t 2193 and 2sbbid 2238 could be proved without ax-12 2170. (Contributed by BJ, 20-Aug-2023.)
Assertion
Ref Expression
bj-nnf-alrim (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))

Proof of Theorem bj-nnf-alrim
StepHypRef Expression
1 bj-nnfa 35910 . 2 (Ⅎ'𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
2 alim 1811 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
31, 2syl9 77 1 (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1538  Ⅎ'wnnf 35905
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1810
This theorem depends on definitions:  df-bi 206  df-an 396  df-bj-nnf 35906
This theorem is referenced by:  bj-stdpc5t  35950  bj-19.21t  35951
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