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	$$⊢\mathrm{Rel}R$$
Assertion	relbrcnv	$$⊢A{R}^{-1}B\leftrightarrow BRA$$

Proof

Step	Hyp	Ref	Expression
1		relbrcnv.1	$$⊢\mathrm{Rel}R$$
2		relbrcnvg	$$⊢\mathrm{Rel}R\to \left(A{R}^{-1}B\leftrightarrow BRA\right)$$
3	1 2	ax-mp	$$⊢A{R}^{-1}B\leftrightarrow BRA$$