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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 3909 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 2610 | . 2 ⊢ (V ∈ 𝐴 → V ∈ V) | |
3 | 1, 2 | mto 620 | 1 ⊢ ¬ V ∈ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 1433 Vcvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: (None) |
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