Theorem 1n0OLD 8527

Description: Obsolete version of 1n0 8526 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 8514	. 2 ⊢ 1o = {∅}
2		0ex 5265	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4737	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3029	1 ⊢ 1o ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2959  ∅c0 4281  {csn 4588  1_oc1o 8500

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-nul 5264

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-v 3456  df-dif 4050  df-un 4154  df-nul 4282  df-sn 4589  df-suc 6389  df-1o 8507

This theorem is used by: (None)