Ifyou want to, we could go to a movie The ability to go to a movie does not depend on "wanting", but the truth of the underlined clause is relevant to the main clause
Examples
Ifyou were wondering, I have your new schedule. "Having your new schedule" does not depend on whether "you were wondering", but the truth of the underlined clause is relevant to the main clause
(logic,grammar) Asubordinate clause, usually introduced byif, that asserts the relevance of the clause to the main clause of the sentence, but not that itentails the main clause; a construction involving such a clause.
2001, Renaat Declerck, Susan Reed,Conditionals: A Comprehensive Empirical Analysis[1], page425:
To be more precise, the speaker of arelevance conditional assumes a mutual understanding on the parts of the speaker and the addressee[s] that the actualization of P is a sufficient condition for the relevance of the Q-utterance.
2013, Tatjana Scheffler,Two-dimensional Semantics: Clausal Adjuncts and Complements, Walter de Gruyter,page124:
For example,relevance conditionals are constructions in conditional shape that do not seem to express a clear conditional meaning at first glance. This has led semanticists to introduce analyses ofrelevance conditionals that capture many of their properties but are very specific to this construction.
A known grammatical marker ofrelevance conditionals is their resistance to linking their antecedent and consequent clauses with 'then': consider the mild oddity of 'If you want biscuits then there are some on the table.'[…]This peculiarity ofrelevance conditionals is straightforwardly explained by the ellipsis theory, according to which the consequent clause doesn't in general express a real (logical) consequent; 'There are some biscuits on the table' is just asserted as true.
antecedent clause that asserts a relevance relationship, not a consequence relationship, to its associated consequent clause; construction comprising such a clause and its consequent
Relevance logic on Wikipedia.Wikipedia