Theorem resdmss

Description: Subset relationship for the domain of a restriction. (Contributed by Scott Fenton, 9-Aug-2024)

	Ref	Expression
Assertion	resdmss	⊢ dom ( 𝐴 ↾ 𝐵 ) ⊆ 𝐵

Proof

Step	Hyp	Ref	Expression
1		dmres	⊢ dom ( 𝐴 ↾ 𝐵 ) = ( 𝐵 ∩ dom 𝐴 )
2		inss1	⊢ ( 𝐵 ∩ dom 𝐴 ) ⊆ 𝐵
3	1 2	eqsstri	⊢ dom ( 𝐴 ↾ 𝐵 ) ⊆ 𝐵