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Mirrors > Home > MPE Home > Th. List > nfntOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nfnt 1767 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfntOLD | ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnf1OLDOLD 2196 | . 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑 | |
2 | df-nfOLD 1712 | . . 3 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) | |
3 | hbnt 2129 | . . 3 ⊢ (∀𝑥(𝜑 → ∀𝑥𝜑) → (¬ 𝜑 → ∀𝑥 ¬ 𝜑)) | |
4 | 2, 3 | sylbi 206 | . 2 ⊢ (Ⅎ𝑥𝜑 → (¬ 𝜑 → ∀𝑥 ¬ 𝜑)) |
5 | 1, 4 | nfdOLD 2181 | 1 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1473 ℲwnfOLD 1700 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-ex 1696 df-nf 1701 df-nfOLD 1712 |
This theorem is referenced by: nfnOLD 2198 nfndOLD 2199 19.23tOLD 2206 |
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