Theorem br0

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

	Ref	Expression
Assertion	br0	⊢ ¬ 𝐴 ∅ 𝐵

Proof

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