That's more or less the same definition I am using - what definition do you think I'm using? Knowledge is a subcategory of belief which can further be expressed as "justified true belief". Knowledge is a specific kind of belief. Perhaps you are using a different definition of knowledge?
Then, if we are using similar definitions, truth is in no way irrelevant to belief--it is integral. It is the object of belief (without that object, taken objectively in the form of proposition, there is no belief).
Further, there can be no attitude of truth towards a proposition if "truth" doesn't serve to describe other propositions, and seem to serve for the present proposition.
Further, the object of belief seems true for a reason. Nothing happens randomly--the object of belief is dependent upon a series (or cascade, depending on your beliefs) of thoughts that preceeded it. (In the case of axiom, the explanation is embedded in justification of the device by which axiom comes about: thought. But that's another story.)
And lastly, the apparent truth of the proposition can only be dependent upon other truthful propositions, since falsehoods cannot produce truth.
I cannot see truth being irrelevant to belief.