"This is my wife."
Translation:Det här är min fru.
Have you gotten the hang of sentences like "det regnar" (it rains)? In such constructions where Swedish requires a subject, Swedish always uses det. It's somewhat the same here, det här is not referring as much to the wife as to the situation of introduction, and in these cases we always use det här.
Saying Denna är min fru sounds a bit.. patriarchal. Sort of like "this one is my wife".
For the same reason we say det in sentences like Det är en hund, 'It is a dog'. det is a formal subject which does not refer to the 'dog' in that sentence, and does not change according to the gender of the thing in the sentence. Detta works the same way, so when it is a formal subject, it is always detta (or det här), never denna (or den här).
This is messing me up for good. If i say "det regnar" i totally agree about the formal subject stuff but if i say "Det är en hund" how can convince myself that "det" doesn't refer to "hund"? It just doesn't make sense to me. The same applies to "This is my wife." where the word "this" refers so obviously to "wife" that i can't really figure out why i should not conjugate it. Is it maybe the fact that the "thing" (the dog or the wife to stick with the examples) have not being mentioned before in the same sentence?