{ k where k is Prime : k divides n } c= NAT

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { k where k is Prime : k divides n } or x in NAT )
assume x in { k where k is Prime : k divides n } ; :: thesis: x in NAT
then ex k being Prime st
( k = x & k divides n ) ;
hence x in NAT by ORDINAL1:def 12; :: thesis: verum

end;

hence { k where k is Prime : k divides n } is Subset of NAT ; :: thesis: verum