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