Biconditional Introduction/Sequent Form/Proof 1

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Theorem

$p \implies q, q \implies p \vdash p \iff q$


Proof

By the tableau method of natural deduction:

$p \implies q, q \implies p \vdash p \iff q$
Line Pool Formula Rule Depends upon Notes
1 1 $p \implies q$ Premise (None)
2 2 $q \implies p$ Premise (None)
3 1, 2 $p \iff q$ Biconditional Introduction: $\iff \mathcal I$ 1, 2

$\blacksquare$