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Metamath Proof Explorer

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	$⊢ A R^{-1} B \leftrightarrow B R A$

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