Full Idea
A conditional is true if the opposite of the conclusion conflicts with the antecedent, and false if it doesn't conflict. Thus 'If it is day, Dion is walking' is false, because 'Dion is not walking' does not conflict with 'It is day'.
Gist of Idea
Conditionals are false if the falsehood of the conclusion does not conflict with the antecedent
Source
report of Stoic school (fragments/reports [c.200 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.73
Book Reference
'The Stoics Reader', ed/tr. Inwood,B/Gerson,L.P. [Hackett 2008], p.19
A Reaction
For the two to conflict there must be some connection in subject matter, which is not the case if the mere falsehood of the conclusion (from a true premise) falsifies the conditional. This seems like a rather good account.