Theorem oldno

Description: An element of an old set is a surreal. (Contributed by Scott Fenton, 27-Feb-2026)

	Ref	Expression
Assertion	oldno	⊢ ( 𝐴 ∈ ( O ‘ 𝐵 ) → 𝐴 ∈ No )

Proof

Step	Hyp	Ref	Expression
1		oldssno	⊢ ( O ‘ 𝐵 ) ⊆ No
2	1	sseli	⊢ ( 𝐴 ∈ ( O ‘ 𝐵 ) → 𝐴 ∈ No )