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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?

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    For then is not a constituent phrase by itself -- it's two words together. For means 'since, because', and then means 'in that case', so together they mean Because, in that case, (i.e, when g = 0), which is perfectly understandable. Jul 2 '20 at 18:26
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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).

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  • Not sure "for then is rather old-fashioned, and is now restricted mainly to religious language," but I agree that the OP's usage of for then is correct. In my experience, for then is not at all uncommon in mathematics. One might read the OP's example as follows: "The result is trivial if g = 0, for it then follows that any basis serves as a set of z's." Jun 18 '20 at 14:32
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"For then" which can mean interval, while is used in informal writings however there is no clause which indicates the existence of "for then". Hence with reference to formal writings, it would be suggestive to use "then" instead of "for then".

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  • Thank you for your help
    – Archie
    Jun 18 '20 at 8:10
  • I am surprised to see "for then" being said to mean "interval" - have you any support for that?
    – Greybeard
    Jun 18 '20 at 8:27

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