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:

1. $\;\bot$ --- premise
2. $\;\varphi\vee\bot$ --- $\vee$ intro 1
3. $\;\bullet\;\bot$ --- assumption
4. $\;\bullet\;\bot$ --- reiteration 3
5. $\;\neg\bot$ --- $\neg$ intro 3 - 4
6. $\;\varphi$ --- MTP 2,5

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

Answer 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.