let X, Y, Z be set ; :: thesis: ( X c= Y implies X /\ Z c= Y /\ Z )
assume A1: X c= Y ; :: thesis: X /\ Z c= Y /\ Z
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in X /\ Z or x in Y /\ Z )
assume A2: x in X /\ Z ; :: thesis: x in Y /\ Z
then x in X by XBOOLE_0:def 4;
then A3: x in Y by A1;
x in Z by A2, XBOOLE_0:def 4;
hence x in Y /\ Z by A3, XBOOLE_0:def 4; :: thesis: verum