Theorem vn0ALT 4345

Description: Alternate proof of vn0 4344. Shorter, but requiring df-clel 2815, ax-8 2109. (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 3483	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4343	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2939  Vcvv 3479  ∅c0 4332

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-v 3481  df-dif 3953  df-nul 4333

This theorem is referenced by: (None)