# Homomorphism proof

## Homework Statement

If f:G$$\rightarrow$$H is a homomorphism, then f(eG) = eH.

## Homework 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

## The Attempt at a Solution

My 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.

Petek
Gold Member
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

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
I feel like an idiot. Thank you!