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 e. On
Assertion	onelssi	|- ( B e. A -> B C_ A )

Proof

Step	Hyp	Ref	Expression
1		on.1	|- A e. On
2		onelss	|- ( A e. On -> ( B e. A -> B C_ A ) )
3	1 2	ax-mp	|- ( B e. A -> B C_ A )