Is how I derive $\bot\vdash \varphi$(rule of esxplosion) from Modus tollendo ponens correct and would you suggest any other way of doing this?

Question

Here's how I'd derive rule of explosion($\bot\vdash\varphi$) from MTP:

Now is it fine and would you suggest any other way of derivation?

@KennyLau I think thou it'd be more neat to prove $\neg\bot$ as a theorem and then use it by theorem introduction in the proof, don't ya think? — Pooria, Sep 27 '17 at 16:19

score 1 · Answer 1 · answered Sep 27 '17 at 13:19

1

This all depends on what rules you have.

For example, in the proof you use $\lor$ Intro, reiteration, and $\neg$ Intro ... how do I know you have those rules available to you?

When you ask whether some proof exists or is correct, you need to tell us what rules you are allowed to use.

answered Sep 27 '17 at 13:19

Bram28

Well assume all rules I use are allowed and any proof in any natural deduction system you'd like is fine ^^ – Pooria Sep 27 '17 at 16:17

1 Answers1