Theorem vn0ALT 4369

Description: Alternate proof of vn0 4368. Shorter, but requiring df-clel 2819, ax-8 2110. (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 3492	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4367	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2946  Vcvv 3488  ∅c0 4352

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ne 2947  df-v 3490  df-dif 3979  df-nul 4353

This theorem is referenced by: (None)