User:Philogo/test table

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Name	Num
Plato	45
Aristotle	23
Hume	21

Premises	Line		Comment
1	1	~(((PvQ) & ~P)⊃ Q)	premis
1	2	((PvQ) & ~P)& ~Q)	1, definition of ⊃
1	3	((P&~P) v (Q&~Q)) & Q	2, de morgan
1	4	((P&~P)&Q) v ((Q&~Q)&Q))	3, de morgan
1	5	(P&~P) v (Q&~Q)	4, weakening
	6	(~(((PvQ) & ~P)⊃ Q) )⊃(P&~P) v (Q&~Q)	1, 5 conditionalising
	7	~((P&~P) v (Q&~Q))	axiom
	8	(((PvQ) & ~P)⊃ Q)	6,7 modus tonens

¬(((P Q) & ¬P)  Q)       premis
((P Q) & ~P)& ~Q)        definition of 

((P&¬P) (Q&~P)) & ¬Q de morgan ((P&¬P)&~Q) ((Q&¬P)&¬Q)) de morgan

(P&~P)  (Q&~Q) weakening    
(¬(((P Q) & ¬P)  Q)) ((P&~P)  (Q&~Q))    
¬ ¬(((PQ) & ¬P))  Q)      mod ton
((PQ) & ¬P))  Q)  QED