Theorem vn0ALT 4301

Description: Alternate proof of vn0 4299. Shorter, but requiring df-clel 2838, ax-8 2145. (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 3459	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4298	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2958  Vcvv 3455  ∅c0 4287

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-v 3457  df-dif 3909  df-nul 4288

This theorem is referenced by: (None)