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QuantifierExistential quantificationExistential quantifierExistential instantiationPredicate calculusRule of inferenceUniversal quantifierMaterial implicationConjunction introductionPropositional logicMathematical inductionIntensional logicLogical biconditionalFirst-order logicLogical consequenceSyllogismDeductionBounded quantificationFormulaConditional proofDescriptive knowledgeInference ruleModus ponensGeneralizationAxiom of extensionalityMonadic second-order logicPredicate logicContrapositionAxiom schemaPrinciple of compositionalityCategorical propositionAxiom schemeModus tollensHypothetical syllogismAxiomatic systemIf and only ifPeirce's lawAxiom of choiceFormal proofSkolem functionProof by contradictionAxiom of unionMathematical proofPropositionLöb's theoremPredicateConditional probabilityPropositional functionAxiom of regularityAxiom schema of specificationVerifiability principleImplicationElementary equivalencePropositional variableProof by exampleAxiomTransitive setModus ponendo ponensUniversal quantificationExtensionalityDisjunction introductionPrinciple of explosionExistential theory of the realsBayes' theoremHigher-order logicAxiom of pairingMathematical logicResolutionSet-builder notationHorn clauseTranscendental argumentsProofEpisyllogismUnconditionalElementTruth tableBoole's inequalityQuantum logicDefinite descriptionClassical logicAxiom schema of replacementTheoryEquivalence classDisjunctive syllogismModus tollendo tollensTheoremSequent calculusLogical conjunctionIdentityLaw of total probabilityBoolean satisfiability problemRelevance logicInductionInductive reasoningConstructible universeMethod of analytic tableauxSubstitutionExistence theoremChain ruleTruth value