Theorem 1n0OLD 8482

Description: Obsolete version of 1n0 8481 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 8469	. 2 ⊢ 1o = {∅}
2		0ex 5275	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4747	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3031	1 ⊢ 1o ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2961  ∅c0 4289  {csn 4594  1_oc1o 8455

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 2148  ax-9 2156  ax-ext 2738  ax-nul 5274

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 2745  df-cleq 2758  df-clel 2841  df-ne 2962  df-v 3460  df-dif 3911  df-un 3913  df-nul 4290  df-sn 4595  df-suc 6373  df-1o 8462

This theorem is used by: (None)