Statement : If you have never been here before then this is your first time.

Proof : (By contradiction). The hypothesis states that "you are here and that you have never been here before" (Note that the "you are here" part is implicit in the statement; we state it explicitly here since it is required in the proof). Required conclusion : "This is your first time".  Let us index the times that you have been here with the natural numbers, (i.e., t₁ is the first time that you have been here, t₂ is the second that you have been here, .... t_n is the n^th time that you have been here,....and so on). Since by hypothesis, you are here, then the set {t₁, t₂, ...t_n, ...} is non-empty. In this sequence of times, {t₁, t₂, ...t_n, ...}, t_{n - 1} is considered to be a time before t_n. We wish to show that this time is time t₁.
    To prove the statement we will suppose that this is not your first time, i.e, this is a time when you are here but this is not the time t₁. Then this must be a time t_n, n a natural number greater then 1. Then n - 1 is an integer greater than 0 and so is a natural number. Then t_{n -1} is a time you were here (since it belongs to the sequence of times above). Since t_{n - 1} both belongs to the sequence of times above AND is considered to be a time before t_n, then you were here before this time t_n. This contradicts our hypothesis which states that you have not been here before. This contradiction arises from supposing that this is not your first time. We must conclude that this IS your first time, i.e, this must be time t₁.

QED
 

NOW do you believe it?

I know I do. (I just hate being confused about such things. Don't you?)