Theorem vn0ALT 4301

Description: Alternate proof of vn0 4300. Shorter, but requiring df-clel 2840, ax-8 2147. (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 3461	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4299	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2960  Vcvv 3457  ∅c0 4288

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-v 3459  df-dif 3910  df-nul 4289

This theorem is referenced by: (None)