Full Idea
A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent.
Gist of Idea
Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent
Source
William D. Hart (The Evolution of Logic [2010], 4)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.90
A Reaction
That is, a proof can be enshrined in an arrow.