Theorem vn0ALT 4331

Description: Alternate proof of vn0 4330. Shorter, but requiring df-clel 2802, ax-8 2100. (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 3470	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4329	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2932  Vcvv 3466  ∅c0 4314

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 3943  df-nul 4315

This theorem is referenced by: (None)