let X, Y, Z be set ; :: thesis: ( X c= Y \/ Z implies X \ Y c= Z )
assume A1: X c= Y \/ Z ; :: thesis: X \ Y c= Z
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in X \ Y or x in Z )
assume A2: x in X \ Y ; :: thesis: x in Z
then x in X by XBOOLE_0:def 5;
then A3: x in Y \/ Z by A1;
not x in Y by A2, XBOOLE_0:def 5;
hence x in Z by A3, XBOOLE_0:def 3; :: thesis: verum