Theorem vn0ALT 4297

Description: Alternate proof of vn0 4296. Shorter, but requiring df-clel 2808, ax-8 2115. (Contributed by NM, 11-Sep-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
vn0ALT	⊢ V ≠ ∅

Proof of Theorem vn0ALT

Step	Hyp	Ref	Expression
1		vex 3442	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4295	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2930  Vcvv 3438  ∅c0 4284

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ne 2931  df-v 3440  df-dif 3902  df-nul 4285

This theorem is referenced by: (None)