Abstract Rule of Inference (推理规则) with Quantifier Universal Modus Ponens Case 1Premise 1∀x(P(x)→Q(x))Premise 2P(a)ConclusionQ(a) Universal Modus Tollens Case 1Premise 1∀x(P(x)→Q(x))Premise 2¬Q(a)Conclusion¬P(a) Universal Transitivity Case 1Premise 1∀x(P(x)→Q(x))Premise 2∀x(Q(x)→R(x))Conclusion∀x(P(x)→R(x)) Existential Instantiation ∃x∈D,P(x) ∴P(a) for some a∈D Universal Instantiation If some property is true of everything in the set, then it is true of any particular thing in the set Core tool for deductive reasoning ∀x∈D,P(x) ∴a∈D→P(a)
