Using Inference Rules to Prove a Query/Goal/Theorem

A proof is a sequence of sentences, where each sentence is either a premise or a sentence derived from earlier sentences in the proof by one of the rules of inference. The last sentence is the query (also called goal or theorem) that we want to prove.

Example for the "weather problem" given above.

1. Q Premise

2. Q => P Premise

3. P Modus Ponens(1,2)

4. (P ^ Q) => R Premise

5. P ^ Q And Introduction(1,2)

6. R Modus Ponens(4,5)

1.	Q	Premise
2.	Q => P	Premise
3.	P	Modus Ponens(1,2)
4.	(P ^ Q) => R	Premise
5.	P ^ Q	And Introduction(1,2)
6.	R	Modus Ponens(4,5)