1.14 $\forall a \in \mathbb{F} \: (-1)a = -a$

Proof:
\begin{align*}
(-1)a &= (-1)a + 0 && \text{(by 1.3)}\\
&=(-1)a + (a + (-a)) && \text{(by 1.4)}\\
&= ((-1)a + a) + (-a) &&\text{(by 1.2)}\\
&= ((-1)a + a1) + (-a) &&\text{(by 1.7)}\\
&= (a(-1) + a1) + (-a) &&\text{(by 1.5)}\\
&= a(-1+1) + (-a) &&\text{(by 1.9)}\\
&= a0 + (-a) &&\text{(by 1.4)}\\
&= 0 + (-a)  &&\text{(by 1.13)}\\
&=-a &&\text{(by 1.12)}\\
\end{align*}