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Metamath Proof Explorer

Theorem sucon

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

		Ref	Expression
	Assertion	sucon	$⊢ suc On = On$

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