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 Th50:
  A\andB\impB\andA in F
  proof
    set P = A\andB;
A1: P\impB in F by Def38;
A2: P\impA in F by Def38;
    ( P\impB )\imp(( P\impA )\imp( P\imp( B\andA ))) in F by Th49;
    then ( P\impA )\imp( P\imp( B\andA )) in F by A1,Def38;
    hence thesis by A2,Def38;
  end;
