Theorem dmcoss2

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

	Ref	Expression
Assertion	dmcoss2	$$⊢\mathrm{dom}\wr R=\mathrm{ran}R$$

Proof

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