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E.g. Modus Ponens (MP)

φ → ψ
φ
ψ


P →(Q →R)
P
Q →R


raining → wet
raining
wet
(P →Q) →R
P → Q
R


wet → slippery
wet
slippery
  • I.e. we can substitute for the metavariables complex sentences
  • Note that, by stringing together applications of rules of inference, it is possible to derive conclusions that cannot be derived in a single step. This idea of stringing together rule applications leads to the notion of a proof.

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