Biconditional Properties

Theorems

Biconditional is Commutative

Formulation 1

$p \iff q \dashv \vdash q \iff p$

Formulation 2

$\vdash \paren {p \iff q} \iff \paren {q \iff p}$

Biconditional is Associative

Formulation 1

$p \iff \paren {q \iff r} \dashv \vdash \paren {p \iff q} \iff r$

Formulation 2

$\vdash \paren {p \iff \paren {q \iff r} } \iff \paren {\paren {p \iff q} \iff r}$

Biconditional is Reflexive

$\vdash p \iff p$