Theorem 1n0OLD 8450

Description: Obsolete version of 1n0 8449 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 8437	. 2 ⊢ 1o = {∅}
2		0ex 5256	. . 3 ⊢ ∅ ∈ V
3	2	snnz 4734	. 2 ⊢ {∅} ≠ ∅
4	1, 3	eqnetri 3026	1 ⊢ 1o ≠ ∅

Syntax hints:   ≠ wne 2956  ∅c0 4285  {csn 4581  1_oc1o 8423

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-nul 5255

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-v 3455  df-dif 3907  df-un 3909  df-nul 4286  df-sn 4582  df-suc 6346  df-1o 8430

This theorem is referenced by: (None)