hypothetical-syllogism-transitive-property

https://en.wikipedia.org/wiki/Hypothetical_syllogism (or transitive property)

A pure hypothetical syllogism is a syllogism in which both premises and the conclusion are all conditional statements. The antecedent of one premise must match the consequent of the other for the conditional to be valid. Consequently, one of the conditionals contains the remained term as antecedent and the other conditional contains the removed term as consequent.

If P, then Q.

If Q, then R.

∴ If P, then R.