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Mirrors > Home > MPE Home > Th. List > dvelimnf | Structured version Visualization version GIF version |
Description: Version of dvelim 2462 using "not free" notation. Usage of this theorem is discouraged because it depends on ax-13 2379. (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 1915 | . 2 ⊢ Ⅎ𝑧𝜓 | |
3 | dvelimnf.2 | . 2 ⊢ (𝑧 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | dvelimf 2459 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ∀wal 1536 Ⅎwnf 1785 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2142 ax-11 2158 ax-12 2175 ax-13 2379 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 |
This theorem is referenced by: nfcvf 2981 nfrab 3339 |
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