Solipsism is the idea that one cannot be sure of anyone's existence but only themself. I think that one can assume this idea to be right and then prove that this is wrong. This self-inconsistency proves it to be wrong. Here is my argument: If solipsism is true, then each person is sure of their existence, i. e. they know that they actually exist. Let's assume mind not to be an illusion. So, each person actually exists, and they know it. Therefore, I could prove that if solipsism is true and mind is no illusion, then each person actually exists. Note that proving that each person actually exists is a contradiction to Solipsism. So I could prove by contradiction that Solipsism is not true.
Is this a valid argument?