Theorem 1one2o

Description: Ordinal one is not ordinal two. Analogous to 1ne2 . (Contributed by AV, 17-Oct-2023)

	Ref	Expression
Assertion	1one2o	⊢ 1o ≠ 2o

Proof

Step	Hyp	Ref	Expression
1		1onn	⊢ 1o ∈ ω
2		omsucne	⊢ ( 1o ∈ ω → 1o ≠ suc 1o )
3	1 2	ax-mp	⊢ 1o ≠ suc 1o
4		df-2o	⊢ 2o = suc 1o
5	3 4	neeqtrri	⊢ 1o ≠ 2o