# Homework Help: Homomorphism proof

1. Dec 12, 2009

### lockedup

1. The problem statement, all variables and given/known data
If f:G$$\rightarrow$$H is a homomorphism, then f(eG) = eH.

2. Relevant equations
The proof from my professor's notes:
f(eG) = f(eG*GeG) = f(eG)*f(eG)
f(eG) = f(eG)*eH
f(eG)*f(eG) = f(eG)*eH
f(eG) = eH

3. The attempt at a solutionMy question is, how do you get from the first line to the second. Because it looks like she's using the proposition to prove itself.

2. Dec 12, 2009

### Petek

The second line doesn't follow from the first. It simply says that if you multiply any element of H by the identity element of H, you get ... (fill in the rest).

Petek

3. Dec 12, 2009

### lockedup

I feel like an idiot. Thank you!