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 Th80:
  (A\orB)\and(A\orC) \imp A\or(B\andC) in F
  proof
    B\imp(C\impB\andC) in F & A\impA in F by Def38,Th34; then
    A\orB\impA\or(C\impB\andC) in F &
    A\or(C\impB\andC)\imp(A\orC\impA\or(B\andC)) in F by Th59,Th79; then
A1: A\orB\imp(A\orC\impA\orB\andC) in F by Th45;
    A\orB\imp(A\orC\impA\orB\andC)\imp((A\orB)\and(A\orC)\impA\orB\andC) in F
    by Th48;
    hence thesis by A1,Def38;
  end;
