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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dvelimv | Structured version Visualization version GIF version |
Description: A version of dvelim 2325 using the "non-free" 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 | nfv 1830 | . . 3 ⊢ Ⅎ𝑥⊤ | |
2 | bj-dvelimv.nf | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜓) |
4 | bj-dvelimv.is | . . 3 ⊢ (𝑧 = 𝑦 → (𝜓 ↔ 𝜑)) | |
5 | 1, 3, 4 | bj-dvelimdv1 32028 | . 2 ⊢ (⊤ → (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑)) |
6 | 5 | trud 1484 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 195 ∀wal 1473 ⊤wtru 1476 Ⅎwnf 1699 |
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-11 2021 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: bj-nfeel2 32030 |
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