Let i be a player with perfect recall in an extensive-form

Question

Let i be a player with perfect recall in an extensive-form game and let bi be a behavior strategy of player i.

Suppose that there is a strategy vector σ_-i of the other players such that ρ(x; b_i, σ_-i) > 0 for each leaf in the game tree.

Prove that there exists a unique mixed strategy σ_i equivalent to b_i.