let X be set ; :: thesis: for Y being real-membered set st X c= Y holds
X is real-membered
let Y be real-membered set ; :: thesis: ( X c= Y implies X is real-membered )
assume A1: X c= Y ; :: thesis: X is real-membered
let x be set ; :: according to MEMBERED:def 3 :: thesis: ( x in X implies x is real )
thus ( x in X implies x is real ) by A1; :: thesis: verum