let X be set ; :: thesis: for Y being complex-membered set st X c= Y holds
X is complex-membered
let Y be complex-membered set ; :: thesis: ( X c= Y implies X is complex-membered )
assume A1: X c= Y ; :: thesis: X is complex-membered
let x be set ; :: according to MEMBERED:def 1 :: thesis: ( x in X implies x is complex )
thus ( x in X implies x is complex ) by A1; :: thesis: verum