Theorem resmpti

Description: Restriction of the mapping operation. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypothesis	resmpti.1	⊢ 𝐵 ⊆ 𝐴
Assertion	resmpti	⊢ ( ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) ↾ 𝐵 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		resmpti.1	⊢ 𝐵 ⊆ 𝐴
2		resmpt	⊢ ( 𝐵 ⊆ 𝐴 → ( ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) ↾ 𝐵 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 ) )
3	1 2	ax-mp	⊢ ( ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) ↾ 𝐵 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 )