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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 5276 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 3465 | . 2 ⊢ (V ∈ 𝐴 → V ∈ V) | |
3 | 1, 2 | mto 196 | 1 ⊢ ¬ V ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2107 Vcvv 3447 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 ax-sep 5260 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3449 |
This theorem is referenced by: curryset 35467 currysetlem3 35470 eliuniincex 43411 eliincex 43412 nvelim 45445 |
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