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 Th60:
  A\impB\imp(C\orA\impC\orB) in F
  proof
    C\impC\orB in F & C\impC\orB\imp(A\impC\orB\imp(C\orA\impC\orB)) in F
    by Def38; then
A1: A\impC\orB\imp(C\orA\impC\orB) in F by Def38;
    A\impB\imp(A\impB) in F & A\impB\imp(A\impB)\imp((A\impB)\andA\impB) in F
    by Th34,Th48; then
    ((A\impB)\andA\impB) in F & B\impC\orB in F by Def38; then
    ((A\impB)\andA\impC\orB) in F &
    ((A\impB)\andA\impC\orB)\imp(A\impB\imp(A\impC\orB)) in F by Th45,Th47;then
    A\impB\imp(A\impC\orB) in F by Def38;
    hence thesis by A1,Th45;
  end;
