Truncated Connectivities in a highly supercritical anisotropic percolation model

We consider an anisotropic bond percolation model on $mathbb{Z}^2$, with $textbf{p}=(p_h,p_v)in [0,1]^2$, $p_v>p_h$, and declare each horizontal (respectively vertical) edge of $mathbb{Z}^2$ to be open with probability $p_h$(respectively $p_v$), and otherwise closed, independently of all other edges. Let $x=(x_1,x_2) in mathbb{Z}^2$ with $0<x_1<x_2$, and $x=(x_2,x_1)in mathbb{Z}^2$. It is natural to ask how the two point connectivity function $prob({0leftrightarrow x})$ behaves, and whether anisotropy in percolation probabilities implies the strict inequality $prob({0leftrightarrow x})>prob({0leftrightarrow x})$. In this note we give an affirmative answer in the highly supercritical regime.