The "Since... then" construction

Is the construction "Since... then" correct? E.g.

Since it's a right triangle, then the Pythagorean theorem holds.

It sounds and feels wrong to me, and I think someone once told me it's wrong, but I haven't been able to find a definitive answer anywhere online. I see this construction used from time to time within mathematics.

Since is synonymous to because in this case. Your sentence is therefore equivalent to

*Because it's a right triangle, then the Pythagorean theorem holds.

There are two words indicating a causal relationship, because and then. That's one too many.

You can use either of these two:

Since it's a right triangle, the Pythagorean theorem holds.
If it's a right triangle(, then) the Pythagorean theorem holds.

Mixing them up (if...then versus since...)is a contamination.

I agree with @oerkelens's answer, except that I would make an allowance for since...then... in cases where there is a lot of verbiage between the two words. such as a list of reasons, a list of steps in the reasoning, or parenthetical statements.

So if St. Paul had followed his usual style, this sentence:

Therefore, since we have so great a cloud of witnesses surrounding us, let us also lay aside every encumbrance...

might have looked like this:

Therefore, since we have so great a cloud of witnesses surrounding us, including Abel, who offered to God a better sacrifice than Cain, through which he obtained the testimony that he was righteous, God testifying about his gifts, and through faith, though he is dead, he still speaks, then let us also lay aside every encumbrance...

As has been remarked "Since p, then q" is a corruption of "if p, then q". The latter is a hypothetical sentence (i.e. it expresses a hypothetical relationship between two states of affairs). "Since", however, is a premise indicator; you'd use it in an argument that is based in the actual state of affairs.

You can see both at work here: "We agreed two weeks ago that if I clean, (then) you clean. Since I in fact cleaned, you must clean."

I suppose that people might mix them up because the difference between hypotheticals and arguments is a subtle one and there are many logical parallels between the two.

I checked out the relevant definition of "then" in the American Heritage Dictionary: "As a consequence; therefore". Using substitution we can see how awkward the "since ..., then ..." construction is: "since [state of affairs], as a consequence [state of affairs]". It just strikes my native-speaker intution that "as a consequence" is preceded by a sentence expressing a state of affairs that is not in a subordinate clause.