let AS be AffinSpace; :: thesis: for a, b being Element of AS holds Line (a,b) c= Line (b,a)
let a, b be Element of AS; :: thesis: Line (a,b) c= Line (b,a)

now

let x be set ; :: thesis: ( x in Line (a,b) implies x in Line (b,a) )
assume A1: x in Line (a,b) ; :: thesis: x in Line (b,a)
then reconsider x9 = x as Element of AS ;
LIN a,b,x9 by A1, Def2;
then LIN b,a,x9 by Th15;
hence x in Line (b,a) by Def2; :: thesis: verum

end;

hence Line (a,b) c= Line (b,a) by TARSKI:def 3; :: thesis: verum