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 Th35:
  A\andB in F iff A in F & B in F
  proof
    A\andB\impA in F & A\andB\impB in F by Def38;
    hence A\andB in F implies A in F & B in F by Def38;
    A\imp(B\impA\andB) in F by Def38; then
    A in F implies B\imp(A\andB) in F by Def38;
    hence thesis by Def38;
  end;
