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Metamath Proof Explorer

Theorem dmcoss2

Description: The domain of cosets is the range. (Contributed by Peter Mazsa, 27-Dec-2018)

		Ref	Expression
	Assertion	dmcoss2	$⊢ dom ≀ R = ran R$

Step	Hyp	Ref	Expression
1		dmcoss3	$⊢ dom ≀ R = dom R^{-1}$
2		df-rn	$⊢ ran R = dom R^{-1}$
3	1 2	eqtr4i	$⊢ dom ≀ R = ran R$