A9: great_dom f,a c= X

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in great_dom f,a or x in X )
assume A10: x in great_dom f,a ; :: thesis: x in X
A11: x in dom f by A10, Def14;
A12: dom f c= X by RELAT_1:def 18;
thus x in X by A11, A12; :: thesis: verum

end;

thus great_dom f,a is Subset of X by A9; :: thesis: verum