Negatives, Reciprocals and the Strict Order in an Ordered Field, as Values

In the setting of Commutative Rings, Fields and Ordered Fields: Standard Notation, let $F$, with operations $+$ and $\cdot$, elements $0$ and $1$ and order $\le$, be an ordered field, and let $x,y\in F$. Write $-x$ for the negative of $x$ and $x^{-1}$ for the reciprocal of $x$ when $x\neq0$; $<$ is the strict relation associated with $\le$.

(i) $-x\in F$ and $x+(-x)=0$.

(ii) If $x\neq0$, then $x^{-1}\in F$ and $x\cdot x^{-1}=1$.

(iii) $x<y$ if and only if $x\le y$ and not $y\le x$.