Exclusive Or with Factor of Exclusive Or

Theorem

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

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

$\dashv \vdash$

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

$\ds $

$\dashv \vdash$

$\ds p \oplus \bot$

$\ds $

$\dashv \vdash$

$\ds p$

$\blacksquare$

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