union F c= D

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in union F or x in D )
assume x in union F ; :: thesis: x in D
then consider Z being set such that
A1: x in Z and
A2: Z in F by TARSKI:def 4;
thus x in D by A1, A2; :: thesis: verum

end;

hence union F is Subset of D ; :: thesis: verum