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

THEOREM    \(P \Leftrightarrow Q,\ P \vdash Q\)
iffD1: ?Q = ?P \(\Longrightarrow\) ?Q \(\Longrightarrow\) ?P

Proof available

THEOREM    \(P \Leftrightarrow Q,\ Q \vdash P\)
iffD2: ?P = ?Q \(\Longrightarrow\) ?Q \(\Longrightarrow\) ?P

Proof available

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