Theorem reseq12i

Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014)

	Ref	Expression
Hypotheses	reseqi.1	$$⊢A=B$$
	reseqi.2	$$⊢C=D$$
Assertion	reseq12i	$$⊢{A\upharpoonright }_C={B\upharpoonright }_D$$

Proof

Step	Hyp	Ref	Expression
1		reseqi.1	$$⊢A=B$$
2		reseqi.2	$$⊢C=D$$
3	1	reseq1i	$$⊢{A\upharpoonright }_C={B\upharpoonright }_C$$
4	2	reseq2i	$$⊢{B\upharpoonright }_C={B\upharpoonright }_D$$
5	3 4	eqtri	$$⊢{A\upharpoonright }_C={B\upharpoonright }_D$$