Dependence

I've been thinking much lately about my dependence upon the Lord. It's commonplace for Christians to say they are absolutely dependent upon God for all things. I've said it. I want to say I believe it. However, this thought has constantly ran through my mind over the past couple of weeks:

Your prayer life will display if you really believe you are dependent upon Him for all things.

What I mean is this. If we truly believed that we were dependent upon Him for everything, would our prayer life not be much better?