Full Idea
If either A or B is true, then you are intuitively justified in believe that If ¬A, B. If you know that ¬(A&B), then you may justifiably infer that if A, ¬B. The truth-functionalist gets both of these cases (disjunction and negated conjunction) correct.
Gist of Idea
Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism
Source
Dorothy Edgington (Conditionals (Stanf) [2006], 2.1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.5
A Reaction
[compressed version] This summarises two of Edgington's three main arguments in favour of the truth-functional account of conditions (along with the existence of Conditional Proof). It is elementary classical logic which supports truth-functionalism.
Related Idea
Idea 14273 Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington]