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Mirrors > Home > NFE Home > Th. List > dvelimc | GIF version |
Description: Version of dvelim 2016 for classes. (Contributed by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
dvelimc.1 | ⊢ ℲxA |
dvelimc.2 | ⊢ ℲzB |
dvelimc.3 | ⊢ (z = y → A = B) |
Ref | Expression |
---|---|
dvelimc | ⊢ (¬ ∀x x = y → ℲxB) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1554 | . . 3 ⊢ Ⅎx ⊤ | |
2 | nftru 1554 | . . 3 ⊢ Ⅎz ⊤ | |
3 | dvelimc.1 | . . . 4 ⊢ ℲxA | |
4 | 3 | a1i 10 | . . 3 ⊢ ( ⊤ → ℲxA) |
5 | dvelimc.2 | . . . 4 ⊢ ℲzB | |
6 | 5 | a1i 10 | . . 3 ⊢ ( ⊤ → ℲzB) |
7 | dvelimc.3 | . . . 4 ⊢ (z = y → A = B) | |
8 | 7 | a1i 10 | . . 3 ⊢ ( ⊤ → (z = y → A = B)) |
9 | 1, 2, 4, 6, 8 | dvelimdc 2510 | . 2 ⊢ ( ⊤ → (¬ ∀x x = y → ℲxB)) |
10 | 9 | trud 1323 | 1 ⊢ (¬ ∀x x = y → ℲxB) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ⊤ wtru 1316 ∀wal 1540 = wceq 1642 Ⅎwnfc 2477 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2479 |
This theorem is referenced by: nfcvf 2512 |
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