Theorem oldnod

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

	Ref	Expression
Hypothesis	oldnod.1	$$⊢\phi \to A\in \mathrm{Old}\left(B\right)$$
Assertion	oldnod	$$⊢\phi \to A\in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		oldnod.1	$$⊢\phi \to A\in \mathrm{Old}\left(B\right)$$
2		oldssno	$$⊢\mathrm{Old}\left(B\right)\subseteq \mathrm{No}$$
3	2 1	sselid	$$⊢\phi \to A\in \mathrm{No}$$