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Mirrors > Home > MPE Home > Th. List > nftht0 | Structured version Visualization version GIF version |
Description: Closed form of nfth 1718. (Contributed by Wolf Lammen, 19-Aug-2018.) (Proof shortened by BJ, 16-Sep-2021.) |
Ref | Expression |
---|---|
nftht0 | ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (∀𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑)) | |
2 | df-nf 1701 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | sylibr 223 | 1 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∃wex 1695 Ⅎwnf 1699 |
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-nf 1701 |
This theorem is referenced by: nfth 1718 nfim1 2055 wl-nfeqfb 32502 |
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