For then - does it exist? [closed]

Example:

The result is trivial if g = 0, for then any basis serves as a set of z's.

Does the phrase exist, or should be there them instead?

Solution 1:

For then is correct. For is an a conjunction approximating to "because" and "then" is an adverb = at that point/in that case.

Thus for then ... = because, in that case, ...

For then is rather old-fashioned, and is now restricted mainly to religious language:

It seemed absurd that the universe be infinite, how could it just go on and on forever? It also seemed absurd that it be finite, for then there would be a wall, and one could wonder about what was beyond it. (The Life of the Cosmos, Lee Smolin 1999).