Theorem resabs2

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

	Ref	Expression
Assertion	resabs2	$$⊢B\subseteq C\to {\left({A\upharpoonright }_B\right)\upharpoonright }_C={A\upharpoonright }_B$$

Proof

Step	Hyp	Ref	Expression
1		rescom	$$⊢{\left({A\upharpoonright }_B\right)\upharpoonright }_C={\left({A\upharpoonright }_C\right)\upharpoonright }_B$$
2		resabs1	$$⊢B\subseteq C\to {\left({A\upharpoonright }_C\right)\upharpoonright }_B={A\upharpoonright }_B$$
3	1 2	eqtrid	$$⊢B\subseteq C\to {\left({A\upharpoonright }_B\right)\upharpoonright }_C={A\upharpoonright }_B$$