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Mirrors > Home > ILE Home > Th. List > nvel | GIF version |
Description: The universal class does not belong to any class. (Contributed by FL, 31-Dec-2006.) |
Ref | Expression |
---|---|
nvel | ⊢ ¬ V ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 4068 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 2700 | . 2 ⊢ (V ∈ 𝐴 → V ∈ V) | |
3 | 1, 2 | mto 652 | 1 ⊢ ¬ V ∈ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 1481 Vcvv 2689 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 ax-sep 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: (None) |
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