Theorem onelssi

Description: A member of an ordinal number is a subset of it. (Contributed by NM, 11-Aug-1994)

	Ref	Expression
Hypothesis	on.1	$$⊢A\in \mathrm{On}$$
Assertion	onelssi	$$⊢B\in A\to B\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		on.1	$$⊢A\in \mathrm{On}$$
2		onelss	$$⊢A\in \mathrm{On}\to \left(B\in A\to B\subseteq A\right)$$
3	1 2	ax-mp	$$⊢B\in A\to B\subseteq A$$