Theorem 1on

Description: Ordinal 1 is an ordinal number. (Contributed by NM, 29-Oct-1995) Avoid ax-un . (Revised by BTernaryTau, 30-Nov-2024)

	Ref	Expression
Assertion	1on	⊢ 1o ∈ On

Proof

Step	Hyp	Ref	Expression
1		df-1o	⊢ 1o = suc ∅
2		0elon	⊢ ∅ ∈ On
3		1oex	⊢ 1o ∈ V
4	1 3	eqeltrri	⊢ suc ∅ ∈ V
5		sucexeloni	⊢ ( ( ∅ ∈ On ∧ suc ∅ ∈ V ) → suc ∅ ∈ On )
6	2 4 5	mp2an	⊢ suc ∅ ∈ On
7	1 6	eqeltri	⊢ 1o ∈ On