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- P → Q
- R → S
- Q → R
- ——–
- P → S

Also referred to as the chain rule, hypothetical syllogism states that if one knows that ’if P then Q’, and ’if R then S’, then one can infer ’if P then S’. For example, if it is known ‘`if it is raining, then it is cloudy`’, and ‘`if it is cloudy, then it is not sunny`’, and ‘`if it is not sunny, then it is cold`’, then hypothetical syllogism allows us to infer that ‘`if it is raining, then it is cold`’. This works with any number of conditional statements, as long as they all follow this pattern.

Hypothetical Syllogism requires at least two references.