Theorem vn0ALT 4338

Description: Alternate proof of vn0 4337. Shorter, but requiring df-clel 2810, ax-8 2108. (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 3478	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4336	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2940  Vcvv 3474  ∅c0 4321

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ne 2941  df-v 3476  df-dif 3950  df-nul 4322

This theorem is referenced by: (None)