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	$$⊢A\in V\to A\mathrm{I}A$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢A=A$$
2		ideqg	$$⊢A\in V\to \left(A\mathrm{I}A\leftrightarrow A=A\right)$$
3	1 2	mpbiri	$$⊢A\in V\to A\mathrm{I}A$$