Theorem ididg

Description: A set is identical to itself. (Contributed by NM, 28-May-2008) (Proof shortened by Andrew Salmon, 27-Aug-2011)

	Ref	Expression
Assertion	ididg	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 I 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		ideqg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 I 𝐴 ↔ 𝐴 = 𝐴 ) )
3	1 2	mpbiri	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 I 𝐴 )