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	$$⊢ARB\to R\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		df-br	$$⊢ARB\leftrightarrow ⟨A,B⟩\in R$$
2		ne0i	$$⊢⟨A,B⟩\in R\to R\ne \varnothing$$
3	1 2	sylbi	$$⊢ARB\to R\ne \varnothing$$