Proof of Agnosticism as a Subset of Atheism Because Both Lead to Non-Belief

We define belief as trust in the unseen to evaluate the belief relationship of agnosticism and atheism. Atheism asserts there is evidence not to believe God exists. Agnosticism asserts that there is no evidence neither to believe nor not to believe God exists. We simplify these definitions by removing God from the mix as the object of belief. The conjectures to test are: Does both atheism and agnosticism imply or lead to non-belief; and Does both atheism and agnosticism imply agnosticism is a subset of atheism. We prove these as theorems. The contra-arguments are found to be not tautologous.