with a view to marriage; with marriage in mind
Used to describe dating, cohabitation, or a relationship that is undertaken with the explicit intention of eventually marrying. Often appears in set phrases like 結婚を前提にお付き合いする.
I'm dating him with marriage in mind.
We started living together with a view to marriage.
A more compact noun form used in similar contexts, e.g. 結婚前提の交際, but 結婚を前提に is the full adverbial phrase.
A set phrase composed of 結婚 (marriage), を (object marker), 前提 (premise/condition), and に (adverbial particle), literally 'on the premise of marriage'.