conjunction. Only if (the stipulation that follows is true).
v. Simple past tense and past participle of provide.
the GNU version of the Collaborative International Dictionary of English
conjunction. On condition; by stipulation; with the understanding; if; -- usually followed by that.
The Century Dictionary and Cyclopedia
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).
Word Usage
"The authors have also included names of companies and products upon occasion, if they thought that mentioning the name provided relevant information for you."