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Mirrors > Home > MPE Home > Th. List > vn0 | Structured version Visualization version GIF version |
Description: The universal class is not equal to the empty set. (Contributed by NM, 11-Sep-2008.) |
Ref | Expression |
---|---|
vn0 | ⊢ V ≠ ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3417 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | ne0ii 4155 | 1 ⊢ V ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2999 Vcvv 3414 ∅c0 4146 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-ne 3000 df-v 3416 df-dif 3801 df-nul 4147 |
This theorem is referenced by: uniintsn 4736 relrelss 5904 imasaddfnlem 16548 imasvscafn 16557 cmpfi 21589 fclscmp 22211 compne 39481 compneOLD 39482 |
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