premises conclusions Implication elimination modus ponens Name of

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表示方法 premises conclusions

表示方法 premises conclusions

Implication – elimination ( modus ponens ) Name of rule

Implication – elimination ( modus ponens ) Name of rule

Conjunction

Conjunction

Negation - introduction 表示推出了一个矛盾 (Falsity)

Negation - introduction 表示推出了一个矛盾 (Falsity)

Negation - elimination

Negation - elimination

Falsity - elimination ex falso sequitur quodlibet anything you want follows from falsity

Falsity - elimination ex falso sequitur quodlibet anything you want follows from falsity

Truth - introduction “true” is true

Truth - introduction “true” is true

Reductio ad absurdum (proof by contradiction):

Reductio ad absurdum (proof by contradiction):

Disjunction

Disjunction

Others Bi-implication Equality

Others Bi-implication Equality

An Example

An Example

Forward and Backward Reasoning!

Forward and Backward Reasoning!

Example Ex.

Example Ex.

The universal quantifier introduction x 不是前提集中的自由变元

The universal quantifier introduction x 不是前提集中的自由变元

The universal quantifier elimination t是对于公式A中的x可代入的项

The universal quantifier elimination t是对于公式A中的x可代入的项

The existential quantifier t是对于公式A中的x可代入的项 y is not free in B, and that the only

The existential quantifier t是对于公式A中的x可代入的项 y is not free in B, and that the only uncanceled hypotheses where y occurs freely are the hypotheses A(y) that are canceled when you apply this rule

Split v. s. Conjunction-introduction

Split v. s. Conjunction-introduction

Destruct v. s. Conjunction-elimination

Destruct v. s. Conjunction-elimination

Destruct v. s. Disjunction-elimination

Destruct v. s. Disjunction-elimination

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