Hypothetical Syllogism
Hypothetical syllogism is a deductively valid form that chains two conditionals into one.
P1) If P, then Q. (P → Q)
P2) If Q, then R. (Q → R)
∴
C) If P, then R. (P → R)
Example
1. If Boots is a cat, then Boots is an animal. 2. If Boots is an animal, then Boots is mortal. ∴ 3. If Boots is a cat, then Boots is mortal.
What's not asserted
Useful for chaining causal or definitional steps. The conclusion is itself a conditional: you haven’t asserted P or R yet, only their connection.