Theorem rnco2

Description: The range of the composition of two classes. (Contributed by NM, 27-Mar-2008)

	Ref	Expression
Assertion	rnco2	⊢ ran ( 𝐴 ∘ 𝐵 ) = ( 𝐴 “ ran 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		rnco	⊢ ran ( 𝐴 ∘ 𝐵 ) = ran ( 𝐴 ↾ ran 𝐵 )
2		df-ima	⊢ ( 𝐴 “ ran 𝐵 ) = ran ( 𝐴 ↾ ran 𝐵 )
3	1 2	eqtr4i	⊢ ran ( 𝐴 ∘ 𝐵 ) = ( 𝐴 “ ran 𝐵 )