UNION (F,G) c= bool T
proof
let x be object ; :: 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
A3: ( X in F & Y in G ) and
A4: x = X \/ Y by SETFAM_1:def 4;
X \/ Y c= T by A3, XBOOLE_1:8;
hence x in bool T by A4; :: thesis: verum
end;
hence UNION (F,G) is Subset-Family of T ; :: thesis: verum