Theorem vn0ALT 4299

Description: Alternate proof of vn0 4298. Shorter, but requiring df-clel 2812, ax-8 2116. (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 3445	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4297	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2933  Vcvv 3441  ∅c0 4286

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-v 3443  df-dif 3905  df-nul 4287

This theorem is referenced by: (None)