let x, y be set ; :: according to TAXONOM2:def 3 :: thesis: ( x in {{} } & y in {{} } & not x c= y & not y c= x implies x misses y )
assume A1: ( x in {{} } & y in {{} } ) ; :: thesis: ( x c= y or y c= x or x misses y )
( x = {} & y = {} ) by A1, TARSKI:def 1;
hence ( x c= y or y c= x or x misses y ) ; :: thesis: verum