Biconditional Properties

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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

$\vdash p \iff p$