This (or it) being understood, conceded, or established; on (this) condition; on these terms: in this sense always introducing a clause of condition or exception, and followed by that (expressed or understood).
the GNU version of the Collaborative International Dictionary of English
conjunction.
On condition; by stipulation; with the understanding; if; -- usually followed by that.
conjunction.
Only if (the stipulation that follows is true).
verb.
Simple past tense and past participle of provide.
Word Usage
"Another clause provided that all persons then in the army, under eighteen and over thirty-five, might return home discharged from the service within ninety days after the act took effect, _provided_, their regiments were filled up with conscripts."