Biconditional


THEOREM   

The biconditional relation is reflexive.

$$\vdash P \Leftrightarrow P$$

Proof available

THEOREM   

The biconditional relation is symmetric.

$$P \Leftrightarrow Q \vdash Q \Leftrightarrow P$$

Proof available

THEOREM   

The biconditional operation is commutative.

$$P \Leftrightarrow Q \dashv\vdash Q \Leftrightarrow P$$

Proof available

THEOREM   

The biconditional relation is transitive.

$$P \Leftrightarrow Q,\ Q \Leftrightarrow R \vdash P \Leftrightarrow R$$

Proof available