While reading Hilbert's Tenth Problem (English version of a talk by Y. Matiyasevich) at page 3 I found:
On the other hand let
$$D(x_1,...,x_m) = 0 \quad (3)$$
be an arbitrary Diophantine equation; suppose that we are looking for its solutions in integers $x_1,...,x_m$. Consider another equation:
$$D(p_1 \Leftrightarrow q_1, ..., p_m \Leftrightarrow q_1) \quad (4)$$
It is clear that any solution of equation (4) in natural numbers $p_1,...,p_m,q_1,...,q_m$ yelds the solution: $x_1 = p_1 \Leftrightarrow q_1, ..., x_m = p_m \Leftrightarrow q_m,$ of equation (3) in integers $x_1,...,x_m$
What is the meaning of the operator $\Leftrightarrow$? Is it a standard notation?
NOTE: the "standard" way to show that a Diophantine equation with integer solutions has a corresponding equivalent Diophantine equation with natural solutions is to use the equation: $$\prod D( \pm x_1, ..., \pm x_m ) = 0$$