Theorem vn0ALT 4281

Description: Alternate proof of vn0 4280. Shorter, but requiring df-clel 2815, ax-8 2121. (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 3436	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4279	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2935  Vcvv 3432  ∅c0 4268

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ne 2936  df-v 3434  df-dif 3893  df-nul 4269

This theorem is referenced by: (None)