let X be set ; :: thesis: for Y being rational-membered set st X c= Y holds
X is rational-membered
let Y be rational-membered set ; :: thesis: ( X c= Y implies X is rational-membered )
assume A1: X c= Y ; :: thesis: X is rational-membered
let x be set ; :: according to MEMBERED:def 4 :: thesis: ( x in X implies x is rational )
thus ( x in X implies x is rational ) by A1; :: thesis: verum