let D be non empty set ; :: thesis: for p, q, r being PartialPredicate of D holds PP_or ((PP_or (p,q)),(PP_or (p,r))) = PP_or ((PP_or (p,q)),r)
let p, q, r be PartialPredicate of D; :: thesis: PP_or ((PP_or (p,q)),(PP_or (p,r))) = PP_or ((PP_or (p,q)),r)
PP_or (p,(PP_or (p,q))) = PP_or ((PP_or (p,p)),q) by Th14;
hence PP_or ((PP_or (p,q)),(PP_or (p,r))) = PP_or ((PP_or (p,q)),r) by Th14; :: thesis: verum