Theorem reseq12d

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

	Ref	Expression
Hypotheses	reseqd.1	$$⊢\phi \to A=B$$
	reseqd.2	$$⊢\phi \to C=D$$
Assertion	reseq12d	$$⊢\phi \to {A\upharpoonright }_C={B\upharpoonright }_D$$

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	$$⊢\phi \to A=B$$
2		reseqd.2	$$⊢\phi \to C=D$$
3	1	reseq1d	$$⊢\phi \to {A\upharpoonright }_C={B\upharpoonright }_C$$
4	2	reseq2d	$$⊢\phi \to {B\upharpoonright }_C={B\upharpoonright }_D$$
5	3 4	eqtrd	$$⊢\phi \to {A\upharpoonright }_C={B\upharpoonright }_D$$