User:Dfeuer/Boolean Lattice forms of Logical Axioms

$p \wedge q \preceq p$

$p \wedge q \preceq q$

$p \preceq p \vee q$

$q \preceq p \vee q$

$(p \vee q) \wedge (r \vee \neg p) \wedge (r \vee \neg q) \preceq r$

$(p \vee q) \wedge \neg p \preceq q$

$\neg (p \wedge q) \wedge p \preceq \neg q$

$p \preceq q \implies \neg p \vee q$