@Protoman2050,

So you are asking whether conditional proofs and RAA proofs (i.e. Reductio ad absurdum -->contradictory proof-->indirect proof) are elaborations of Modus ponens and Modus Tollens?

Honestly, they may look the same in format but they are nothing alike in structure (in my opinion). Modus ponens for example infers Q from P and P-->Q and thus only infers the consequent. A conditional, which requires the formation of a conditional, infers the whole thing, antecedent and consequent. Indirect proof wise, modus Tollens would have you conclude in the negated antecedent from a negated consequent. But in the case of the indirect proof, you can infer anything when you derive a contradiction. The Modus Tollens inference rule will only let you infer the negated antecedent.

On a side note, you may want to spell out the inference rule or the type of logical syntactical structure because there are

*many**as long as* you negate both variables. You need to correct #3. This needs to corrected because you entire proof rests on the A wrongly inferred from line 3.