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Metamath Proof Explorer

Theorem fvresi

Description: The value of a restricted identity function. (Contributed by NM, 19-May-2004)

		Ref	Expression
	Assertion	fvresi	$⊢ B \in A \to ({I ↾}_{A}) (B) = B$

Step	Hyp	Ref	Expression
1		fvres	$⊢ B \in A \to ({I ↾}_{A}) (B) = I (B)$
2		fvi	$⊢ B \in A \to I (B) = B$
3	1 2	eqtrd	$⊢ B \in A \to ({I ↾}_{A}) (B) = B$