Theorem vn0ALT 4309

Description: Alternate proof of vn0 4308. Shorter, but requiring df-clel 2803, ax-8 2111. (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 3451	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4307	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2925  Vcvv 3447  ∅c0 4296

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-v 3449  df-dif 3917  df-nul 4297

This theorem is referenced by: (None)