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Metamath Proof Explorer

Theorem reloprab

Description: An operation class abstraction is a relation. (Contributed by NM, 16-Jun-2004)

		Ref	Expression
	Assertion	reloprab	$⊢ Rel \{⟨⟨x, y⟩, z⟩ \| φ\}$

Step	Hyp	Ref	Expression
1		dfoprab2	$⊢ \{⟨⟨x, y⟩, z⟩ \| φ\} = \{⟨w, z⟩ \| \exists x \exists y (w = ⟨x, y⟩ \land φ)\}$
2	1	relopabiv	$⊢ Rel \{⟨⟨x, y⟩, z⟩ \| φ\}$