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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfntht2 | Structured version Visualization version GIF version |
Description: Closed form of nfnth 1719. (Contributed by BJ, 6-May-2019.) |
Ref | Expression |
---|---|
bj-nfntht2 | ⊢ (∀𝑥 ¬ 𝜑 → ℲℲ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 398 | . 2 ⊢ (∀𝑥 ¬ 𝜑 → (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑)) | |
2 | bj-nf3 31767 | . 2 ⊢ (ℲℲ𝑥𝜑 ↔ (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑)) | |
3 | 1, 2 | sylibr 223 | 1 ⊢ (∀𝑥 ¬ 𝜑 → ℲℲ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∀wal 1473 ℲℲwnff 31764 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-or 384 df-ex 1696 df-bj-nf 31765 |
This theorem is referenced by: bj-nfnth 31774 |
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