Theorem onun2i

Description: The union of two ordinal numbers is an ordinal number. (Contributed by NM, 13-Jun-1994)

	Ref	Expression
Hypotheses	on.1	⊢ 𝐴 ∈ On
	on.2	⊢ 𝐵 ∈ On
Assertion	onun2i	⊢ ( 𝐴 ∪ 𝐵 ) ∈ On

Proof

Step	Hyp	Ref	Expression
1		on.1	⊢ 𝐴 ∈ On
2		on.2	⊢ 𝐵 ∈ On
3		onun2	⊢ ( ( 𝐴 ∈ On ∧ 𝐵 ∈ On ) → ( 𝐴 ∪ 𝐵 ) ∈ On )
4	1 2 3	mp2an	⊢ ( 𝐴 ∪ 𝐵 ) ∈ On