Theorem resabs2d

Description: Absorption law for restriction. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	resabs2d.1	$$⊢\phi \to B\subseteq C$$
Assertion	resabs2d	$$⊢\phi \to {\left({A\upharpoonright }_B\right)\upharpoonright }_C={A\upharpoonright }_B$$

Proof

Step	Hyp	Ref	Expression
1		resabs2d.1	$$⊢\phi \to B\subseteq C$$
2		resabs2	$$⊢B\subseteq C\to {\left({A\upharpoonright }_B\right)\upharpoonright }_C={A\upharpoonright }_B$$
3	1 2	syl	$$⊢\phi \to {\left({A\upharpoonright }_B\right)\upharpoonright }_C={A\upharpoonright }_B$$