Theorem onelond

Description: An element of an ordinal number is an ordinal number. Theorem 2.2(iii) of BellMachover p. 469. Lemma 1.3 of Schloeder p. 1. Deduction form. (Contributed by Scott Fenton, 31-Jul-2026)

	Ref	Expression
Hypotheses	onelond.1	|- ( ph -> A e. On )
	onelond.2	|- ( ph -> B e. A )
Assertion	onelond	|- ( ph -> B e. On )

Proof

Step	Hyp	Ref	Expression
1		onelond.1	|- ( ph -> A e. On )
2		onelond.2	|- ( ph -> B e. A )
3		onelon	|- ( ( A e. On /\ B e. A ) -> B e. On )
4	1 2 3	syl2anc	|- ( ph -> B e. On )