Exclusive Or with Factor of Exclusive Or

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Theorem

$\left({p \oplus q}\right) \oplus q \dashv \vdash p$


Proof

\(\ds \left({p \oplus q}\right) \oplus q\) \(\dashv \vdash\) \(\ds p \oplus \left({q \oplus q}\right)\) Exclusive Or is Associative
\(\ds \) \(\dashv \vdash\) \(\ds p \oplus \bot\) Exclusive Or with Itself
\(\ds \) \(\dashv \vdash\) \(\ds p\) Exclusive Or with Contradiction

$\blacksquare$


Sources