If .. then is very common, both in everyday speech and in technical language, for example the language of computers where it has a precise meaning, see this explanation in
Wikipedia, as it does in formal logic -
Wikipedia again.
I'm surprised by your statement though that
most of the time we just see "If....., ...." . Think about it - where do you see it "most of the time" ? In textbooks? Remember - the language served up in textbooks is often very simplified in terms of actual language use.
Here are all the examples of
If sentences that I found in one article from the
Daily Telegraph. (Excuse the reactionary tone - it's just what came up on Google).
If we take away risk, then capitalism is finished
If you don't want to accept that you might lose money at capitalism, then don't play the game.
If not, capitalism is over.
If only we had a serious opposition party to embrace, champion and uphold the vital values of capitalism, the cure might come far faster, and be far more durable.
Two with, two without. For me the addition of
then simply emphasises the conclusion - which is, after all, what
then marks.
But it's certainly not "ungrammatical" and if someone's told you that it is, then I'm afraid they're wrong.
As for the comma - looking at the first twelve pages of "if-then" results for Google, there are almost no instances of the structure being used without it - except in a couple of cases where the writer doesn't seem to use much punctuation at all. But again, it's not a matter of grammaticality. The use of commas in English is fairly flexible - they tend to be used if in the spoken language there would be a pause - for example after a longish subordinate clause. And as an
if clause is a subordinate clause which is frequently fairly long, then the probability of a pause/comma is quite high.
Notice that I've just used a sentence with
as ... then. If you stop thinking of
If sentences as fixed structures, then the problem is resolved. Like any subordinating conjunction, an
if clause can be tagged on to any main clause. There's no rule that says what happens in the first cluase determines what happens in the second - the two are independent, and any two clauses can combine as long as they're semantically compatible - ie as long as the meaning makes sense. So there's no
grammatical difference between eg:
If John has arrived, then we'll start.
As John has arrived, then we'll start.
Then introduces a result, which is equally compatible with a condition or a cause.
Hope that helps.
If-then Clause 
Linear Mode
