Theorem onelssd

Description: An element of an ordinal number is a subset of the number. Deduction form. (Contributed by Scott Fenton, 31-Jul-2026)

	Ref	Expression
Hypotheses	onelssd.1	$$⊢\phi \to A\in \mathrm{On}$$
	onelssd.2	$$⊢\phi \to B\in A$$
Assertion	onelssd	$$⊢\phi \to B\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		onelssd.1	$$⊢\phi \to A\in \mathrm{On}$$
2		onelssd.2	$$⊢\phi \to B\in A$$
3		onelss	$$⊢A\in \mathrm{On}\to \left(B\in A\to B\subseteq A\right)$$
4	1 2 3	sylc	$$⊢\phi \to B\subseteq A$$