Theorem brne0

Description: If two sets are in a binary relation, the relation cannot be empty. (Contributed by Alexander van der Vekens, 7-Jul-2018)

	Ref	Expression
Assertion	brne0	⊢ ( 𝐴 𝑅 𝐵 → 𝑅 ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		df-br	⊢ ( 𝐴 𝑅 𝐵 ↔ ⟨ 𝐴 , 𝐵 ⟩ ∈ 𝑅 )
2		ne0i	⊢ ( ⟨ 𝐴 , 𝐵 ⟩ ∈ 𝑅 → 𝑅 ≠ ∅ )
3	1 2	sylbi	⊢ ( 𝐴 𝑅 𝐵 → 𝑅 ≠ ∅ )