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	|- ( ph -> A e. On )
	onelssd.2	|- ( ph -> B e. A )
Assertion	onelssd	|- ( ph -> B C_ A )

Proof

Step	Hyp	Ref	Expression
1		onelssd.1	|- ( ph -> A e. On )
2		onelssd.2	|- ( ph -> B e. A )
3		onelss	|- ( A e. On -> ( B e. A -> B C_ A ) )
4	1 2 3	sylc	|- ( ph -> B C_ A )