Theorem reseq1d

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

	Ref	Expression
Hypothesis	reseqd.1	$$⊢\phi \to A=B$$
Assertion	reseq1d	$$⊢\phi \to {A\upharpoonright }_C={B\upharpoonright }_C$$

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	$$⊢\phi \to A=B$$
2		reseq1	$$⊢A=B\to {A\upharpoonright }_C={B\upharpoonright }_C$$
3	1 2	syl	$$⊢\phi \to {A\upharpoonright }_C={B\upharpoonright }_C$$