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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dvelimv | Structured version Visualization version GIF version |
Description: A version of dvelim 2465 using the "nonfree" idiom. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-dvelimv.nf | ⊢ Ⅎ𝑥𝜓 |
bj-dvelimv.is | ⊢ (𝑧 = 𝑦 → (𝜓 ↔ 𝜑)) |
Ref | Expression |
---|---|
bj-dvelimv | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-dvelimv.nf | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜓) |
3 | bj-dvelimv.is | . . 3 ⊢ (𝑧 = 𝑦 → (𝜓 ↔ 𝜑)) | |
4 | 2, 3 | bj-dvelimdv1 34073 | . 2 ⊢ (⊤ → (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑)) |
5 | 4 | mptru 1535 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 207 ∀wal 1526 ⊤wtru 1529 Ⅎwnf 1775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-11 2151 ax-12 2167 ax-13 2381 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 |
This theorem is referenced by: bj-nfeel2 34075 |
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