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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnf-alrim | Structured version Visualization version GIF version |
Description: Proof of the closed form of alrimi 2212 from modalK (compare alrimiv 1927). See also bj-alrim 34046. Actually, most proofs between 19.3t 2200 and 2sbbid 2246 could be proved without ax-12 2176. (Contributed by BJ, 20-Aug-2023.) |
Ref | Expression |
---|---|
bj-nnf-alrim | ⊢ (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnfa 34079 | . 2 ⊢ (Ⅎ'𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
2 | alim 1810 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl9 77 | 1 ⊢ (Ⅎ'𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 Ⅎ'wnnf 34074 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-4 1809 |
This theorem depends on definitions: df-bi 209 df-an 399 df-bj-nnf 34075 |
This theorem is referenced by: bj-stdpc5t 34116 bj-19.21t 34117 |
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