Theorem rnresi

Description: The range of the restricted identity function. (Contributed by NM, 27-Aug-2004)

	Ref	Expression
Assertion	rnresi	$$⊢\mathrm{ran}\left({\mathrm{I}\upharpoonright }_A\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		df-ima	$$⊢\mathrm{I}\left[A\right]=\mathrm{ran}\left({\mathrm{I}\upharpoonright }_A\right)$$
2		imai	$$⊢\mathrm{I}\left[A\right]=A$$
3	1 2	eqtr3i	$$⊢\mathrm{ran}\left({\mathrm{I}\upharpoonright }_A\right)=A$$