So, the question becomes, is the conclusion of an argument necessarily connected with its premises?
My thoughts on this example, is that arguments which take the form of premises and a conclusion are not, in themselves, "matters of fact" as Hume defines them, but are "relations of ideas". The argument may be about a matter of fact, but the nature of the argument itself is a relation of ideas and depends on the logical structure of the argument and the meanings of the words used. I therefore think that Hume would say that the form of an argument can be known a priori, but the conclusion of an argument about a matter of fact can never be known a priori.
I will try and clarify this with an example. Take the argument "if the water in the glass is freezing then the temperature must be at or below zero degrees centigrade".
The argument is about a matter of fact, but we cannot tell from the premise that the conclusion necessarily follows. Even where the argument employs a law of nature such as 'water freezes at or below zero degrees centigrade', Hume would argue that conclusion does not necessarily follow from the premise if it is a contingent fact, and it could just as easily be otherwise (logically speaking).
If we assume that the law of nature in question is universal, then the conclusion does follow. Hume would say that this assumption is just that, a contingent idea which results from the constant conjunction of freezing temperatures with frozen water.
I am struggling to formulate why I think Hume may not be right in the instance of laws of nature, because my personal view is that when they are employed in arguments, there is some form of necessary connection between the premises and the conclusion - either because language has petrified certain truths (as Wittgenstein might say) or because the connection is innate (as Descartes might say), or because reason has super-imposed the necessary connection of cause and effect (as Kant would say).