Both constructions are commonly used in mathematics. In standard (not mathematical) present-day English, these would be written as…

we have the fact that B = C. Consider:

We

have the fact that John is an idiot.
*Well, John is gonna get mad at everyone.
Is John an Idiot?

Which would they be in, in fact, neither the latter two constructions would be admissible in ordinary English, and I can’t find any evidence in Google books that they ever were admissible (although the middle one sounds marginally better to me, which means that if you had to choose one of these two, I would recommend that one). Since A is true, we learn that B = C.

Since A is true, we know that B = C. (or any
other way of expressing this that are also grammatical in
ordinary English) Notice that I have dropped “the fact” from

the first part of the sentence.

I hate John Stewart. He’s an idiot. What’s wrong with what he

said?
Is John Slade an idiot?

I don’t believe the second part of the original sentence is even accepted in mathematical English.

EDIT: I just realized that maybe you meant “since the fact A is true” to be parsed as “since (the fact A) is true” rather than “since the fact (A is true)”. If that is the case, you can ignore the second part of my answer.