Theorem vn0ALT 4303

Description: Alternate proof of vn0 4301. Shorter, but requiring df-clel 2841, ax-8 2148. (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 3462	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4300	1 ⊢ V ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2961  Vcvv 3458  ∅c0 4289

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-ne 2962  df-v 3460  df-dif 3911  df-nul 4290

This theorem is used by: (None)