Theorem vn0ALT 4293

Description: Alternate proof of vn0 4292. Shorter, but requiring df-clel 2831, ax-8 2138. (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 3452	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4291	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2951  Vcvv 3448  ∅c0 4280

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-ext 2728

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1557  df-fal 1567  df-ex 1794  df-sb 2085  df-clab 2735  df-cleq 2748  df-clel 2831  df-ne 2952  df-v 3450  df-dif 3902  df-nul 4281

This theorem is referenced by: (None)