Standard Axiom Schemata for Propositional Logic
Implication Introduction: s => (t => s)
Implication Distribution: (r => (s => t)) => ((r => s) => (r => t))
Conflict Resolution: (~t=>~s) => ((~t=>s)=>t)
(s<=>t) => (s=>t)
(s<=>t) => (t=>s)
(t=>s) => ((s=>t) => (s<=>t)
(s<=t) <=> (t=>s)
(s|t) <=> (~s=>t)
(s&t) <=> ~(~s|~t)