Conjunction


THEOREM   

Conjunction is idempotent.

$$P \wedge P \dashv\vdash P$$

Proof available

THEOREM    \(P \vdash P \wedge P\)

Proof available

THEOREM    \(P \wedge P \vdash P\)

Proof available

THEOREM   

Conjunction is commutative.

$$P \wedge Q \dashv\vdash Q \wedge P$$

Proof available

THEOREM   

Conjunction is associative.

$$P \wedge Q \wedge R \dashv\vdash P \wedge (Q \wedge R)$$

Proof available

LEMMA   

Conjunction is left self-distributive.

$$P \wedge (Q \wedge R) \dashv\vdash (P \wedge Q) \wedge (P \wedge R)$$

Proof available

LEMMA   

Conjunction is right self-distributive.

$$(Q \wedge R) \wedge P \dashv\vdash (Q \wedge P) \wedge (R \wedge P)$$

Proof available

THEOREM   

Conjunction is self-distributive.

Proof available