let x, y, X be set ; :: thesis: ( not x in X & not y in X implies X = (X \/ {x,y}) \ {x,y} )
assume
( not x in X & not y in X )
; :: thesis: X = (X \/ {x,y}) \ {x,y}
then
( (X \/ {x,y}) \ {x,y} = X \ {x,y} & X \ {x,y} = X )
by Th144, XBOOLE_1:40;
hence
X = (X \/ {x,y}) \ {x,y}
; :: thesis: verum