Theorem resmpti

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

	Ref	Expression
Hypothesis	resmpti.1	$$⊢B\subseteq A$$
Assertion	resmpti	$$⊢{\left(x\in A⟼C\right)\upharpoonright }_B=\left(x\in B⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		resmpti.1	$$⊢B\subseteq A$$
2		resmpt	$$⊢B\subseteq A\to {\left(x\in A⟼C\right)\upharpoonright }_B=\left(x\in B⟼C\right)$$
3	1 2	ax-mp	$$⊢{\left(x\in A⟼C\right)\upharpoonright }_B=\left(x\in B⟼C\right)$$