Minor qualification of Gary's assertion: There are standard first-order systems where the deduction theorem does not hold unconditionally (e.g., the system in Mendelson's Introduction to Mathematical Logic or Ted Sider's Logic for Philosophy). Specifically, in such systems, premises can contain free variables and the rule of Generalization is unrestricted.  Hence, e.g., (x)Fx is provable from the premise Fx but the corresponding conditional Fx -> (x)Fx is not a theorem (rightly so, of course, as it is not valid in standard first-order model theory). Thus, in such systems, the corresponding conditional for a deductively valid argument is provable only in those cases where the conclusion of the argument can be derived in such a way that no application of Generalization results in the quantification of a variable that occurs free in one of the premises. (This is actually not quite true, but close enough to get at the idea; see Mendelson for a precise statement of the conditions.) Systems in which the deduction theorem does hold without qualification instead (in effect) simply disallow such applications of Generalization in the first place.