"provided only that" is correct and usable in written English.
You can use it to introduce a condition that needs to be met before something else can happen. For example: We can offer you a loan, provided only that you pass a credit check.
The subsequent steps in the consent process, with specific patient consent forms for each molecular cohort and for each treatment, avoided information overload and provided only that information that was specifically relevant to the particular patient.
However small the probability, provided only that it be finite, the mathematical expectation of this wager is infinite.
There would be employment of some kind: of any kind, he didn't much mind what, provided only that he was capable of whatever it was.
To encourage the residents back, town hall offered a guilder-for-guilder subsidy for renovation work, provided only that it had official approval.
Nick operates in a world without scarcity: his magical elves can make anything he needs, in whatever quantity, provided only that you deserve it.
After all, time travellers of whatever period will be able to attend, provided only that news of the convention survives into any future period that might invent time travel.
For example, People for the Ethical Treatment of Animals will provide only that information which supports their cause, whereas the U.S. Fish and Wildlife Services might provide the same family of information without agenda bias.
Mr. Uzzell can teach you to write providing only that somebody else has been able to teach you to spell.
The air traffic control recordings are less strictly privileged: section 29 of the same act provides only that they may not be used in certain legal proceedings.
So we followed the guidelines and provided only the care that seemed necessary: medicine and follow-up.
aValues are provided only for factors that were independently associated with unprotected anal sex in the final multivariate model.
