let X, Y be set ; :: thesis: ( X c= Y implies X /\ Y = X )
assume A1: X c= Y ; :: thesis: X /\ Y = X
thus X /\ Y c= X by Th17; :: according to XBOOLE_0:def 10 :: thesis: X c= X /\ Y
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in X or x in X /\ Y )
assume A2: x in X ; :: thesis: x in X /\ Y
then x in Y by A1;
hence x in X /\ Y by A2, XBOOLE_0:def 4; :: thesis: verum