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 Th59:
  A\impB in F & C\impD in F implies A\orC\impB\orD in F
  proof
    assume A1: A\impB in F;
    assume A2: C\impD in F;
A3: A\impB\orD\imp(C\impB\orD\imp(A\orC\impB\orD)) in F by Def38;
    B\impB\orD in F & D\impB\orD in F by Def38; then
A4: A\impB\orD in F & C\impB\orD in F by A1,A2,Th45; then
    C\impB\orD\imp(A\orC\impB\orD) in F by A3,Def38;
    hence A\orC\impB\orD in F by A4,Def38;
  end;
