Theorem 1n0OLD 8499

Description: Obsolete version of 1n0 8498 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 8486	. 2 ⊢ 1o = {∅}
2		0ex 5260	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4733	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3025	1 ⊢ 1o ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2955  ∅c0 4278  {csn 4584  1_oc1o 8472

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-nul 5259

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-v 3452  df-dif 4047  df-un 4151  df-nul 4279  df-sn 4585  df-suc 6368  df-1o 8479

This theorem is used by: (None)