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Mirrors > Home > MPE Home > Th. List > nvel | Structured version Visualization version 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 5211 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 3512 | . 2 ⊢ (V ∈ 𝐴 → V ∈ V) | |
3 | 1, 2 | mto 199 | 1 ⊢ ¬ V ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2110 Vcvv 3494 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-ext 2793 ax-sep 5195 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-v 3496 |
This theorem is referenced by: curryset 34252 currysetlem3 34255 eliuniincex 41368 eliincex 41369 nvelim 43316 |
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