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Hypothetical Syllogism , also known as Transitivity of Material Conditional and Chain Argument is a valid rule of inference of propositional logic and valid argument form that has the following form:

P1: If P, then Q.

P2: If Q, then R.

C: Therefore, If P then R.

This is expressed in rule form as:


\frac{P \rightarrow Q, Q \rightarrow R}
{\therefore, P \rightarrow R}

and in sequent notation as:

P \to Q, Q \to R \vdash P \to R

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