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Mirrors > Home > MPE Home > Th. List > dvelimnf | Structured version Visualization version GIF version |
Description: Version of dvelim 2472 using "not free" notation. Usage of this theorem is discouraged because it depends on ax-13 2389. (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 1914 | . 2 ⊢ Ⅎ𝑧𝜓 | |
3 | dvelimnf.2 | . 2 ⊢ (𝑧 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | dvelimf 2469 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 208 ∀wal 1534 Ⅎwnf 1783 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-10 2144 ax-11 2160 ax-12 2176 ax-13 2389 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1539 df-ex 1780 df-nf 1784 |
This theorem is referenced by: nfcvf 3010 nfrab 3389 |
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