The phrase, "a very old building," combines the two sentences using an appositive phrase. In this case, ''a very old building'' is the appositive phrase because it provides more information.
If you need a further explanation, read the quoted text below:
"An appositive is a noun or pronoun that renames or identifies another noun or pronoun in some way. An appositive phrase consists of an appositive and its modifiers. An appositive phrase can be either essential (restrictive) or nonessential (nonrestrictive)."
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