Theorem residm

Description: Idempotent law for restriction. (Contributed by NM, 27-Mar-1998)

	Ref	Expression
Assertion	residm	⊢ ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐵 ) = ( 𝐴 ↾ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		ssid	⊢ 𝐵 ⊆ 𝐵
2		resabs2	⊢ ( 𝐵 ⊆ 𝐵 → ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐵 ) = ( 𝐴 ↾ 𝐵 ) )
3	1 2	ax-mp	⊢ ( ( 𝐴 ↾ 𝐵 ) ↾ 𝐵 ) = ( 𝐴 ↾ 𝐵 )