constructive dilemma
Two conditionals plus "one condition or the other" give "one result or the other."
Constructive dilemma is the valid form: if P, then Q; if R, then S; P or R; therefore Q or S. It works like modus ponens applied to two conditionals at once.
Examples
"If I take the bus, I'm late. If I drive, I pay for parking. I'll take the bus or drive. So I'm late or I pay for parking."
See also