Theorem omsson

Description: Omega is a subset of On . (Contributed by NM, 13-Jun-1994) (Proof shortened by Andrew Salmon, 27-Aug-2011)

	Ref	Expression
Assertion	omsson	$$⊢\mathrm{\omega }\subseteq \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		dfom2	$$⊢\mathrm{\omega }=\left\{x\in \mathrm{On}|\mathrm{suc}x\subseteq \left\{y\in \mathrm{On}|\neg \mathrm{Lim}y\right\}\right\}$$
2	1	ssrab3	$$⊢\mathrm{\omega }\subseteq \mathrm{On}$$