Theorem 1ons

Description: Surreal one is a surreal ordinal. (Contributed by Scott Fenton, 18-Mar-2025)

	Ref	Expression
Assertion	1ons	⊢ 1s ∈ Ons

Proof

Step	Hyp	Ref	Expression
1		1no	⊢ 1s ∈ No
2		right1s	⊢ ( R ‘ 1s ) = ∅
3		elons	⊢ ( 1s ∈ Ons ↔ ( 1s ∈ No ∧ ( R ‘ 1s ) = ∅ ) )
4	1 2 3	mpbir2an	⊢ 1s ∈ Ons