Theorem rnresss

Description: The range of a restriction is a subset of the whole range. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Assertion	rnresss	⊢ ran ( 𝐴 ↾ 𝐵 ) ⊆ ran 𝐴

Proof

Step	Hyp	Ref	Expression
1		resss	⊢ ( 𝐴 ↾ 𝐵 ) ⊆ 𝐴
2	1	rnssi	⊢ ran ( 𝐴 ↾ 𝐵 ) ⊆ ran 𝐴