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Mirrors > Home > ILE Home > Th. List > nvel | GIF version |
Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.) |
Ref | Expression |
---|---|
nvel | ⊢ ¬ V ∈ A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 3879 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 2560 | . 2 ⊢ (V ∈ A → V ∈ V) | |
3 | 1, 2 | mto 587 | 1 ⊢ ¬ V ∈ A |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 1390 Vcvv 2551 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-13 1401 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 ax-sep 3866 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: (None) |
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