Disjunction in terms of NOR

Theorem

$p \lor q \dashv \vdash \paren {p \downarrow q} \downarrow \paren {p \downarrow q}$

where $\lor$ denotes logical disjunction and $\downarrow$ denotes logical NOR.

Proof

\(\ds p \lor q\)

\(\dashv \vdash\)

\(\ds \neg \neg \paren {p \lor q}\)

Double Negation

\(\ds \)

\(\dashv \vdash\)

\(\ds \neg \paren {p \downarrow q}\)

Definition of Logical NOR

\(\ds \)

\(\dashv \vdash\)

\(\ds \paren {p \downarrow q} \downarrow \paren {p \downarrow q}\)

NOR with Equal Arguments

$\blacksquare$