reserve X,Y for set, x,y,z for object, i,j,n for natural number;
reserve
  n for non empty Nat,
  S for non empty non void n PC-correct PCLangSignature,
  L for language MSAlgebra over S,
  F for PC-theory of L,
  A,B,C,D for Formula of L;

theorem Th79:
  C\or(A\impB)\imp(C\orA\impC\orB) in F
  proof
A1: C\imp(C\orA\impC\orB)\imp((A\impB\imp(C\orA\impC\orB))\imp
    (C\or(A\impB)\imp(C\orA\impC\orB))) in F by Def38;
    C\impC\orB in F by Def38; then
    C\orA\imp(C\impC\orB) in F &
    C\orA\imp(C\impC\orB)\imp(C\imp(C\orA\impC\orB)) in F by Th44,Th41; then
    C\imp(C\orA\impC\orB) in F by Def38; then
A2: (A\impB\imp(C\orA\impC\orB))\imp(C\or(A\impB)\imp(C\orA\impC\orB)) in F
    by A1,Def38;
    A\impB\imp(C\orA\impC\orB) in F by Th60;
    hence thesis by A2,Def38;
  end;
