UNION F,G c= bool T

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in UNION F,G or x in bool T )
assume x in UNION F,G ; :: thesis: x in bool T
then consider X, Y being set such that
A2: ( X in F & Y in G & x = X \/ Y ) by SETFAM_1:def 4;
X \/ Y c= T by A2, XBOOLE_1:8;
hence x in bool T by A2; :: thesis: verum

end;

hence UNION F,G is Subset-Family of T ; :: thesis: verum