Theorem rnresi

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

	Ref	Expression
Assertion	rnresi	⊢ ran ( I ↾ 𝐴 ) = 𝐴

Proof

Step	Hyp	Ref	Expression
1		df-ima	⊢ ( I “ 𝐴 ) = ran ( I ↾ 𝐴 )
2		imai	⊢ ( I “ 𝐴 ) = 𝐴
3	1 2	eqtr3i	⊢ ran ( I ↾ 𝐴 ) = 𝐴