Provided, conj.
On condition; by stipulation; with the understanding; if; -- usually followed by that; as, provided that nothing in this act shall prejudice the rights of any person whatever. Provided the deductions are logical, they seem almost indifferent to their truth. G. H. Lewes.
Note: This word is strictly a participle, and the word being is understood, the participle provided agreeing with the whole sentence absolute, and being equivalent to this condition being previously stipulated or established.
Shades of meaning
Fernald has no entry of its own for provided; he lists it under but.
Where he writes about it:
So may the use of but in the sense of unless; as, "it never rains but it pours." To the same head must be referred the conditional use; as, "you may go, but with your father's consent" (i. e., "provided you have," "except that you must have," etc.). — from but