let y, x be set ; :: thesis: for a, b being Object of (1Cat (x,y)) holds Hom (a,b) = {y}
let a, b be Object of (1Cat (x,y)); :: thesis: Hom (a,b) = {y}
thus Hom (a,b) c= {y} ; :: according to XBOOLE_0:def 10 :: thesis: {y} c= Hom (a,b)
y is Morphism of (1Cat (x,y)) by TARSKI:def 1;
then y in Hom (a,b) by CAT_1:11;
hence {y} c= Hom (a,b) by ZFMISC_1:31; :: thesis: verum