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Metamath Proof Explorer

Theorem br0

Description: The empty binary relation never holds. (Contributed by NM, 23-Aug-2018)

		Ref	Expression
	Assertion	br0	$⊢ \neg A \emptyset B$

Step	Hyp	Ref	Expression
1		noel	$⊢ \neg ⟨A, B⟩ \in \emptyset$
2		df-br	$⊢ A \emptyset B \leftrightarrow ⟨A, B⟩ \in \emptyset$
3	1 2	mtbir	$⊢ \neg A \emptyset B$