Propositional logic


THEOREM (Law of noncontradiction)    \(\neg (P \wedge \neg P)\)

Proof available

THEOREM (Law of excluded middle)    \(P \vee \neg P\)

Proof available

LEMMA    \(P \vee Q \vdash \neg P \Rightarrow Q\)

Proof available

LEMMA    \(\neg P \Rightarrow Q \vdash P \vee Q\)

Proof available

THEOREM    \(P \vee Q \dashv\vdash \neg P \Rightarrow Q\)

Proof available

THEOREM    \(P \Rightarrow Q \vdash \neg P \vee Q\)

Proof available

THEOREM    \(\neg P \vee Q \vdash P \Rightarrow Q\)

Proof available

THEOREM    \(\neg P \Rightarrow \neg Q \vdash Q \Rightarrow P\)

Proof available

LEMMA    \(P \Rightarrow \neg Q \vdash Q \Rightarrow \neg P\)

Proof available

LEMMA    \(Q \Rightarrow \neg P \vdash P \Rightarrow \neg Q\)

Proof available