TITLE: Is there a better alternative to the phrase, 'it holds that'?
QUESTION [11 upvotes]: The following phrases abound in my writing:

There exists [whatever] such that [whatever].
For all [whatever] it holds that [whatever].

Lately, I've been feeling that the phrase 'it holds that' is overly long-winded. The only substitute I can think of is 'we have that' which is just as bad. I've solved the problem in my personal writing by using the abbreviation 'iht = it holds that' (along with sth = such that), but this isn't appropriate for more formal pieces.
Is there a better phrase?

REPLY [11 votes]: Personally, I would recommend not saying things like "It holds that" which few, if any, native English speakers would say.  Instead, say "we have that" or just "we have", or perhaps replace "It holds that x > y" with "The inequality x > y holds".
Similarly, I would recommend not saying things like "We denote by x the distance between y and z".  Instead, say "We let x denote the distance between y and z".