Theorem vn0ALT 4352

Description: Alternate proof of vn0 4351. Shorter, but requiring df-clel 2814, ax-8 2108. (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 3482	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4350	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2938  Vcvv 3478  ∅c0 4339

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-v 3480  df-dif 3966  df-nul 4340

This theorem is referenced by: (None)