let x, y be object ; :: thesis: for X being set holds
( X \ {x,y} = {} iff ( X = {} or X = {x} or X = {y} or X = {x,y} ) )
let X be set ; :: thesis: ( X \ {x,y} = {} iff ( X = {} or X = {x} or X = {y} or X = {x,y} ) )
( X \ {x,y} = {} iff X c= {x,y} ) by XBOOLE_1:37;
hence ( X \ {x,y} = {} iff ( X = {} or X = {x} or X = {y} or X = {x,y} ) ) by Lm13; :: thesis: verum