Try another, but this time use the terms theism, weak atheism and strong atheism.
It wouldn't make any difference. It is a proof of what follows from your definition of weak atheism and therefore in order to be incorrect you have to show how it is
logically invalid. The proof
CANNOT be wrong because a line/step in the proof says something you consider wrong as
this is what inference rules in logical proofs are for: to show what is
necessary according to logic itself.
Let me attempt more clearly. Most swans are white, but there are black swans (in Australia, if memory serves).
Imagine I argue the following:
All swans are white birds (premise)
If a bird is not white, then it isn't a swan.
If bird is a swan, then it is white.
The argument is wrong, but it is only wrong because the premise isn't true. The other two statements are justified
entirely and completely on
logic itself and the premise. My premises were your definitions. For me to be wrong
logic itself must be wrong.
Let me be a little more comprehensive. When logicians say that an argument or proof is valid, it means that if the premises are true, then the conclusion or conclusions are
necessarily true. What I said above about swans is valid, because if the premise were true, then
logic itself necessitates that the other two statements are true. The
only reason they can be wrong is if the premise is, and indeed it is (there are black swans).
When confronted with a proof like the one I gave you, there are only two possible ways the conclusion could be wrong. One is if the premises are not true. However, they're you're definitions, so presumably that isn't an option. The other way is for the proof to contain an inference (going from one line to another) for which there is no inference/logic rule. For example:
If a bird is a crow, then it is black (premise)
**If a bird is black, it is a crow. (false conclusion)
The reason the conclusion is incorrect is because it is illogical, meaning there is no inference rule to justify the step
If A then B
therefore
if B then A
However, there is one which says
If A then B
therefore
If not B, the not A
For the proof to be wrong you'd have to show what step or steps were
illogical, meaning there is no
inference rule that can justify that step or steps.