TheoremEdit
Let f be a homomorphism from group G to group K.
Let e_{G} and e_{K} be identities of G and K.
 f(e_{G}) = e_{K}
ProofEdit

0. f maps to K 1. inverse in K . 2. f is a homomorphism 3. identity e_{G} . 4. 1. . 5. identity e_{K}, definition of inverse 6. identity e_{K}