In a PhD thesis, I would like to express that I am the first one who has proved the result. Is it right to say "For the first time we show..."?
In a paper with multiple authors I would say that this is correct (and almost the only time you would use the active voice), but I just can't see it for a solo work - one author logically fits with I show.
You can always keep to the passive voice ("It is shown for the first time in this work that..."). Also is it the first time - if you have published this result before writing up, you may want to say that ("It was shown for the first time [me et al. 2013] that...")