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Metamath Proof Explorer

Theorem mptrel

Description: The maps-to notation always describes a binary relation. (Contributed by Scott Fenton, 16-Apr-2012)

		Ref	Expression
	Assertion	mptrel	$⊢ Rel (x \in A ⟼ B)$

Step	Hyp	Ref	Expression
1		df-mpt	$⊢ (x \in A ⟼ B) = \{⟨x, y⟩ \| (x \in A \land y = B)\}$
2	1	relopabiv	$⊢ Rel (x \in A ⟼ B)$