Theorem onsuci

Description: The successor of an ordinal number is an ordinal number. Inference associated with onsuc and onsucb . Corollary 7N(c) of Enderton p. 193. (Contributed by NM, 12-Jun-1994)

	Ref	Expression
Hypothesis	onssi.1	⊢ 𝐴 ∈ On
Assertion	onsuci	⊢ suc 𝐴 ∈ On

Proof

Step	Hyp	Ref	Expression
1		onssi.1	⊢ 𝐴 ∈ On
2		onsuc	⊢ ( 𝐴 ∈ On → suc 𝐴 ∈ On )
3	1 2	ax-mp	⊢ suc 𝐴 ∈ On