let X be set ; :: thesis: ( X is natural-membered implies X is integer-membered )
assume A1: X is natural-membered ; :: thesis: X is integer-membered
let x be object ; :: according to MEMBERED:def 5 :: thesis: ( x in X implies x is integer )
assume x in X ; :: thesis: x is integer
then x is natural by A1;
then x in omega by ORDINAL1:def 12;
hence x in INT by NUMBERS:17; :: according to INT_1:def 2 :: thesis: verum