let G, H be Group; :: thesis: for g being Homomorphism of G,H holds Image g = gr (rng g)
let g be Homomorphism of G,H; :: thesis: Image g = gr (rng g)
( rng g = the carrier of (Image g) & the carrier of (Image g) = carr (Image g) ) by Th44;
hence Image g = gr (rng g) by GROUP_4:31; :: thesis: verum