Theorem elon

Description: An ordinal number is an ordinal set. (Contributed by NM, 5-Jun-1994)

	Ref	Expression
Hypothesis	elon.1	⊢ 𝐴 ∈ V
Assertion	elon	⊢ ( 𝐴 ∈ On ↔ Ord 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elon.1	⊢ 𝐴 ∈ V
2		elong	⊢ ( 𝐴 ∈ V → ( 𝐴 ∈ On ↔ Ord 𝐴 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∈ On ↔ Ord 𝐴 )