Theorem relbrcnv

Description: When R is a relation, the sethood assumptions on brcnv can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Hypothesis	relbrcnv.1	⊢ Rel 𝑅
Assertion	relbrcnv	⊢ ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		relbrcnv.1	⊢ Rel 𝑅
2		relbrcnvg	⊢ ( Rel 𝑅 → ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 )