Theorem 1n0OLD 8461

Description: Obsolete version of 1n0 8460 as of 10-Jun-2026. (Contributed by NM, 26-Dec-2004.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
1n0OLD	⊢ 1o ≠ ∅

Proof of Theorem 1n0OLD

Step	Hyp	Ref	Expression
1		df1o2 8448	. 2 ⊢ 1o = {∅}
2		0ex 5262	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4738	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3030	1 ⊢ 1o ≠ ∅

Syntax hints:   ≠ wne 2960  ∅c0 4288  {csn 4585  1_oc1o 8434

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737  ax-nul 5261

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-v 3459  df-dif 3910  df-un 3912  df-nul 4289  df-sn 4586  df-suc 6356  df-1o 8441

This theorem is referenced by: (None)