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Mirrors > Home > MPE Home > Th. List > vn0ALT | Structured version Visualization version GIF version |
Description: Alternate proof of vn0 4331. Shorter, but requiring df-clel 2802, ax-8 2100. (Contributed by NM, 11-Sep-2008.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vn0ALT | ⊢ V ≠ ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3470 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | ne0ii 4330 | 1 ⊢ V ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2932 Vcvv 3466 ∅c0 4315 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-ne 2933 df-v 3468 df-dif 3944 df-nul 4316 |
This theorem is referenced by: (None) |
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