What is Logic? #28: Reductio Ad Absurdum

Doctor Logic Awkwardly Does Logic: What is Logic?
Video #28: Reductio Ad Absurdum

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[roychess]

Here is my attempt at the case of BAROCO syllogistic proof:
1 M a P Premise
2 M o S Premise / the conclusion to prove is P o S.
3 P a S Assumption
4 M a P Reiteration, 1
5 P a S Reiteration, 3
6 M a S Barbara, 4, 5 [a contradictory pair on lines 6 and 7]
7 M o S Reiteration, 2 [contradicts line 6 above]
8 It is not the case that P a S. [Didn't know how to write the symbolic version --the bar notation on top -- on the computer]
Basically, P a S the original assumption (line 3) can be denied due to the appearance of a contradiction in the proof. Thus P o S must be true.
QED