Is there a verb meaning "suffice" and "require" simultaneously?

Question

Out of curiosity, is there a verb, which need not be popular, such that it says "suffice" and "require" simultaneously? I am after a verb that is equivalent to "if and only if".

The major context that originated this problem is a mathematics one. For example, a minimal workable one, the equivalence "The equation x+3=5 holds if and only if x = 2" can be said in another way as "for the equation x + 3 = 5 to hold requires that x = 2 and, for the equation x+3=5 to hold, it suffices that x = 2" (as one can easily check).

The most preferred verb of such a kind is a one that can be used to directly replace "if and only if" everywhere. I mean, if V is such a verb, then "x+3=5 if and only if x = 2" should be equivalent to "x+3=5 V x=2".

Answer 1

Is there a verb meaning “suffice” and “require” simultaneously?
If V is such a verb, then "x+3=5 if and only if x = 2" should be equivalent to "x+3=5 V x=2".

The answer to this question is No. There is no such verb that means "is true only when".

Answer 2

Such a verb inherently doesn't exist that would work in the context you are presenting. Grammatically, the mathematical expressions you are attempting to link are clauses, specifically independent clauses of the form "[subject] [verb]s [object]". Purdue's guidelines on clauses indicate that independent clauses can only be linked by either a conjunction or a special marking word. Using a verb to connect the independent clauses "x+3=5" and "x=2" would not be grammatical. The correct way to link those would be a conjunction. "If and only if" works as a conjunction here, but if you want one that's less formal other conjunctions that are close include "only when", "exclusively when", and "whenever".

If you want a word that works in a different context, a different example might be useful.

Answer 3

I'm going to quote Wikipedia, even though it's not something I would normally do:

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

In that it is biconditional (a statement of material equivalence), the connective can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false). It is controversial whether the connective thus defined is properly rendered by the English "if and only if", with its pre-existing meaning. There is nothing to stop one from stipulating that we may read this connective as "only if and if", although this may lead to confusion.

In writing, phrases commonly used, with debatable propriety, as alternatives to P "if and only if" Q include Q is necessary and sufficient for P, P is equivalent (or materially equivalent) to Q (compare material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. Some authors regard "iff" as unsuitable in formal writing; others use it freely. . . .

The corresponding logical symbols are "↔", "⇔", and "≡", and sometimes "iff". These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas (e.g., in metalogic). In Łukasiewicz's notation, it is the prefix symbol 'E'.

But after all of that, I agree with the other answer that, with respect to normal English, the simple answer is "No. There is no single verb."