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Metamath Proof Explorer

Theorem mptresid

Description: The restricted identity relation expressed in maps-to notation. (Contributed by FL, 25-Apr-2012)

		Ref	Expression
	Assertion	mptresid	$⊢ {I ↾}_{A} = (x \in A ⟼ x)$

Step	Hyp	Ref	Expression
1		opabresid	$⊢ {I ↾}_{A} = \{⟨x, y⟩ \| (x \in A \land y = x)\}$
2		df-mpt	$⊢ (x \in A ⟼ x) = \{⟨x, y⟩ \| (x \in A \land y = x)\}$
3	1 2	eqtr4i	$⊢ {I ↾}_{A} = (x \in A ⟼ x)$