reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem Th50:
  X /\ (Y \ Z) = X /\ Y \ X /\ Z
proof
A1: X /\ Y c= X by Th17;
  X /\ Y \ X /\ Z = ((X /\ Y) \ X) \/ ((X /\ Y) \ Z) by Lm2
    .= {} \/ ((X /\ Y) \ Z) by A1,Lm1
    .= (X /\ Y) \ Z;
  hence thesis by Th49;
end;
