Theorem elong

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

	Ref	Expression
Assertion	elong	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ On ↔ Ord 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		ordeq	⊢ ( 𝑥 = 𝐴 → ( Ord 𝑥 ↔ Ord 𝐴 ) )
2		df-on	⊢ On = { 𝑥 ∣ Ord 𝑥 }
3	1 2	elab2g	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ On ↔ Ord 𝐴 ) )