Theorem oldnod

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

	Ref	Expression
Hypothesis	oldnod.1	⊢ ( 𝜑 → 𝐴 ∈ ( O ‘ 𝐵 ) )
Assertion	oldnod	⊢ ( 𝜑 → 𝐴 ∈ No )

Proof

Step	Hyp	Ref	Expression
1		oldnod.1	⊢ ( 𝜑 → 𝐴 ∈ ( O ‘ 𝐵 ) )
2		oldssno	⊢ ( O ‘ 𝐵 ) ⊆ No
3	2 1	sselid	⊢ ( 𝜑 → 𝐴 ∈ No )