Theorem resabs1i

Description: Absorption law for restriction. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	resabs1i.1	$$⊢B\subseteq C$$
Assertion	resabs1i	$$⊢{\left({A\upharpoonright }_C\right)\upharpoonright }_B={A\upharpoonright }_B$$

Proof

Step	Hyp	Ref	Expression
1		resabs1i.1	$$⊢B\subseteq C$$
2		resabs1	$$⊢B\subseteq C\to {\left({A\upharpoonright }_C\right)\upharpoonright }_B={A\upharpoonright }_B$$
3	1 2	ax-mp	$$⊢{\left({A\upharpoonright }_C\right)\upharpoonright }_B={A\upharpoonright }_B$$