Theorem vn0ALT 4292

Description: Alternate proof of vn0 4290. Shorter, but requiring df-clel 2835, ax-8 2146. (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 3454	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4289	1 ⊢ V ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2955  Vcvv 3450  ∅c0 4278

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-v 3452  df-dif 4047  df-nul 4279

This theorem is used by: (None)