let G, H be Group; :: thesis: for g being Homomorphism of G,H holds g . (1_ G) = 1_ H
let g be Homomorphism of G,H; :: thesis: g . (1_ G) = 1_ H
g . (1_ G) = g . ((1_ G) * (1_ G)) by GROUP_1:def 4
.= (g . (1_ G)) * (g . (1_ G)) by Def6 ;
hence g . (1_ G) = 1_ H by GROUP_1:7; :: thesis: verum