Theorem sucon

Description: The class of all ordinal numbers is its own successor. (Contributed by NM, 12-Sep-2003)

	Ref	Expression
Assertion	sucon	$$⊢\mathrm{suc}\mathrm{On}=\mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		onprc	$$⊢\neg \mathrm{On}\in \mathrm{V}$$
2		sucprc	$$⊢\neg \mathrm{On}\in \mathrm{V}\to \mathrm{suc}\mathrm{On}=\mathrm{On}$$
3	1 2	ax-mp	$$⊢\mathrm{suc}\mathrm{On}=\mathrm{On}$$