Theorem 1n0OLD 8480

Description: Obsolete version of 1n0 8479 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 8467	. 2 ⊢ 1o = {∅}
2		0ex 5261	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4737	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3026	1 ⊢ 1o ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2956  ∅c0 4279  {csn 4584  1_oc1o 8453

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 2147  ax-9 2155  ax-ext 2733  ax-nul 5260

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 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-v 3453  df-dif 3902  df-un 3904  df-nul 4280  df-sn 4585  df-suc 6361  df-1o 8460

This theorem is used by: (None)