let X, Y, Z be set ; :: thesis: X \ (Y /\ Z) = (X \ Y) \/ (X \ Z)
thus X \ (Y /\ Z) c= (X \ Y) \/ (X \ Z) :: according to XBOOLE_0:def 10 :: thesis: (X \ Y) \/ (X \ Z) c= X \ (Y /\ Z)

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in X \ (Y /\ Z) or x in (X \ Y) \/ (X \ Z) )
assume A1: x in X \ (Y /\ Z) ; :: thesis: x in (X \ Y) \/ (X \ Z)
then not x in Y /\ Z by XBOOLE_0:def 5;
then A2: ( not x in Y or not x in Z ) by XBOOLE_0:def 4;
x in X by A1, XBOOLE_0:def 5;
then ( x in X \ Y or x in X \ Z ) by A2, XBOOLE_0:def 5;
hence x in (X \ Y) \/ (X \ Z) by XBOOLE_0:def 3; :: thesis: verum

end;

( X \ Y c= X \ (Y /\ Z) & X \ Z c= X \ (Y /\ Z) ) by Th17, Th34;
hence (X \ Y) \/ (X \ Z) c= X \ (Y /\ Z) by Th8; :: thesis: verum