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 Th96:
  A\imp(B\impC) in F & D\impB in F implies A\imp(D\impC) in F
  proof
    assume
A1: A\imp(B\impC) in F & D\impB in F;
    (A\imp(B\impC))\imp(B\imp(A\impC)) in F by Th41; then
    B\imp(A\impC) in F by A1,Def38; then
A2: D\imp(A\impC) in F by A1,Th45;
    (D\imp(A\impC))\imp(A\imp(D\impC)) in F by Th41;
    hence thesis by A2,Def38;
  end;
