Proviso

Etymology

From the Medieval Latin phrase "proviso quod" (it being provided that), the opening words of conditional clauses in legal documents. Its root is "providere" (to foresee, provide for), the same source as "provide" and "prudent."

noun · /pruh-VY-zoh/
A condition or stipulation attached to an agreement.
What it names
A single word for the "but only if" clause — the string attached to a deal or promise.
Example
She agreed to fund the trip, with the proviso that he keep every receipt.
Related idea
A proviso sets a condition on an agreement; a caveat is more a warning attached to it — one limits the deal, the other flags a risk within it.