let C be Category; :: thesis: for a, b being Object of C st Hom (a,b) <> {} holds
for f being Morphism of a,b holds opp (f opp) = f
let a, b be Object of C; :: thesis: ( Hom (a,b) <> {} implies for f being Morphism of a,b holds opp (f opp) = f )
assume A1: Hom (a,b) <> {} ; :: thesis: for f being Morphism of a,b holds opp (f opp) = f
then A2: Hom ((b opp),(a opp)) <> {} by Th5;
let f be Morphism of a,b; :: thesis: opp (f opp) = f
thus opp (f opp) = f opp by A2, Def7
.= f by A1, Def6 ; :: thesis: verum