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 Th69:
  A\imp(B\impC) in F & C\impD in F implies A\imp(B\impD) in F
  proof assume
A1: A\imp(B\impC) in F & C\impD in F;
    A\imp(B\impC)\imp(A\andB\impC) in F by Th48;
    then A\andB\impC in F by A1,Def38;
    then A\andB\impD in F & A\andB\impD\imp(A\imp(B\impD)) in F
    by A1,Th45,Th47;
    hence thesis by Def38;
  end;
