Theorem onssnel2i

Description: An ordering law for ordinal numbers. (Contributed by NM, 13-Jun-1994)

	Ref	Expression
Hypothesis	on.1	$$⊢A\in \mathrm{On}$$
Assertion	onssnel2i	$$⊢B\subseteq A\to \neg A\in B$$

Proof

Step	Hyp	Ref	Expression
1		on.1	$$⊢A\in \mathrm{On}$$
2	1	onirri	$$⊢\neg A\in A$$
3		ssel	$$⊢B\subseteq A\to \left(A\in B\to A\in A\right)$$
4	2 3	mtoi	$$⊢B\subseteq A\to \neg A\in B$$