Theorem vn0ALT 4340

Description: Alternate proof of vn0 4339. Shorter, but requiring df-clel 2806, ax-8 2101. (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 3475	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4338	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2937  Vcvv 3471  ∅c0 4323

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-v 3473  df-dif 3950  df-nul 4324

This theorem is referenced by: (None)