Biconditional with Factor of Biconditional

Theorem

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

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

$\dashv \vdash$

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

$\ds $

$\dashv \vdash$

$\ds p \iff \top$

$\ds $

$\dashv \vdash$

$\ds p$

$\blacksquare$

2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.10$: Exercise $2.4$