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 Th38:
  A\imp(B\impC) in F implies B\imp(A\impC) in F
  proof
    assume
A1: A\imp(B\impC) in F;
A2: ((A\impB)\imp(A\impC))\imp((B\imp(A\impB))\imp(B\imp(A\impC))) in F
    by Th37;
    (A\imp(B\impC))\imp((A\impB)\imp(A\impC)) in F by Def38;
    then ((A\impB)\imp(A\impC)) in F by A1,Def38;
    then
A3: ((B\imp(A\impB))\imp(B\imp(A\impC))) in F by A2,Def38;
    B\imp(A\impB) in F by Def38;
    hence thesis by A3,Def38;
  end;
