First Order Logic: Everybody has an initial position

Question

I'm having difficulty expressing the following thought in first order logic.

I want to say that every agent has an initial position and I'd express it as this (using words):

For All agent of type Agents, There Exists an x of type xCoordinate and an y of type yCoordinate such that I_Position(agent,x,y) AND Tile(x,y)

Or in idp:

!ag[agent]: ? xCo[xCo],yCo[yCo]: I_position(ag, xCo, yCo) & Tile(xCo,yCo).

With tile being an expression for a valid tile, a valid position.

Problem with this expression is that I've been learned that an For All expression is ALWAYS with an implication (=>) and a There Exists expression is always with an And (&).

Obviously, I don't have an implication. Does this sentence do what I think it does?