let X be set ; :: thesis: for Y being natural-membered set st X c= Y holds
X is natural-membered
let Y be natural-membered set ; :: thesis: ( X c= Y implies X is natural-membered )
assume A1: X c= Y ; :: thesis: X is natural-membered
let x be set ; :: according to MEMBERED:def 6 :: thesis: ( x in X implies x is natural )
thus ( x in X implies x is natural ) by A1; :: thesis: verum