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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	⊢ ¬ 𝐴 ∅ 𝐵

Step	Hyp	Ref	Expression
1		noel	⊢ ¬ ⟨ 𝐴 , 𝐵 ⟩ ∈ ∅
2		df-br	⊢ ( 𝐴 ∅ 𝐵 ↔ ⟨ 𝐴 , 𝐵 ⟩ ∈ ∅ )
3	1 2	mtbir	⊢ ¬ 𝐴 ∅ 𝐵