Theorem brcnv

Description: The converse of a binary relation swaps arguments. Theorem 11 of Suppes p. 61. (Contributed by NM, 13-Aug-1995)

	Ref	Expression
Hypotheses	opelcnv.1	$$⊢A\in \mathrm{V}$$
	opelcnv.2	$$⊢B\in \mathrm{V}$$
Assertion	brcnv	$$⊢A{R}^{-1}B\leftrightarrow BRA$$

Proof

Step	Hyp	Ref	Expression
1		opelcnv.1	$$⊢A\in \mathrm{V}$$
2		opelcnv.2	$$⊢B\in \mathrm{V}$$
3		brcnvg	$$⊢\left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)\to \left(A{R}^{-1}B\leftrightarrow BRA\right)$$
4	1 2 3	mp2an	$$⊢A{R}^{-1}B\leftrightarrow BRA$$