let X be set ; :: thesis: ( X is complex-membered implies X c= COMPLEX )
assume A1: X is complex-membered ; :: thesis: X c= COMPLEX
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in X or x in COMPLEX )
assume x in X ; :: thesis: x in COMPLEX
then x is complex by A1;
hence x in COMPLEX ; :: thesis: verum