game theory – Showing an inequality involiving min,max

Question: Given the two-person zero sum game represented by the matrix,
$ A = begin{bmatrix}
x & y \
z & g
end{bmatrix} $
.

Show that $min(x,y,z) leq value of A leq max(x,y,z)$(*).

I know that if there is no saddle point, then either $x > y, y < z, z > g$ and $d < x$, or $x < y, y > z, z<g$ and $g>x$. And the value for 2×2 games is given by
$$v = cfrac{xg-yz}{x-y+g-z}$$

I thought of examining 9 cases (for each min. and max) and showing that (*) holds. Is there any simpler way? Thanks in advance.