reserve X,Y,Z,Z1,Z2,D for set,x,y for object;

theorem
  meet {X,Y} = X /\ Y
proof
A1: X in {X,Y} & Y in {X,Y} by TARSKI:def 2;
  for x being object holds x in meet {X,Y} iff x in X & x in Y
  proof let x be object;
    thus x in meet {X,Y} implies x in X & x in Y by A1,Def1;
    assume x in X & x in Y;
    then for Z holds Z in {X,Y} implies x in Z by TARSKI:def 2;
    hence thesis by Def1;
  end;
  hence thesis by XBOOLE_0:def 4;
end;
