We explore ways that university students handle proving statements that have the overall structure of a conditional implies a conditional, i.e., (p [right arrow] q) [implies] (r [right arrow] s). We structure our analysis using the theory of conceptual blending. We find conceptual blending useful for describing the creation of powerful new ideas necessary for proof construction as well as for describing the creation of blends that slow or hinder student efforts at proof construction. [For the complete proceedings, see ED585874.]