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Metamath Proof Explorer

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	$⊢ A \in V \to A I A$

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