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 Th46:
  C\imp(B\impA) in F & B in F implies C\impA in F
  proof
    assume that
A1: C\imp(B\impA) in F and
A2: B in F;
    (C\imp(B\impA))\imp(B\imp(C\impA)) in F by Th41;
    then B\imp(C\impA) in F by A1,Def38;
    hence thesis by A2,Def38;
  end;
