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Mirrors > Home > MPE Home > Th. List > dvelimnf | Structured version Visualization version GIF version |
Description: Version of dvelim 2444 using "not free" notation. Usage of this theorem is discouraged because it depends on ax-13 2365. (Contributed by Mario Carneiro, 9-Oct-2016.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dvelimnf.1 | ⊢ Ⅎ𝑥𝜑 |
dvelimnf.2 | ⊢ (𝑧 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
dvelimnf | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvelimnf.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | nfv 1909 | . 2 ⊢ Ⅎ𝑧𝜓 | |
3 | dvelimnf.2 | . 2 ⊢ (𝑧 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | dvelimf 2441 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 205 ∀wal 1531 Ⅎwnf 1777 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-11 2146 ax-12 2163 ax-13 2365 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-nf 1778 |
This theorem is referenced by: nfcvf 2926 nfrab 3466 |
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