What does one say?

[Ryft]

Wrong, and typical of theistic sleight of hand. There is no first burden of proof associated with the position that "god exists" is false ...

1. Truth claims shoulder the burden of proof (given).
2. If Atheist says, "The proposition 'God exists' is not true," then Atheist has made a truth claim (conditional).
3. Atheist says, "The proposition 'God exists' is not true" (given).
4. Therefore, Atheist has made a truth claim (from 2 and 3).
5. Therefore, Atheist shoulders the burden of proof (from 1 and 4).

This argument is valid, and it is sound if 2 can be supported. So then...

6. If "God exists" is not true, then "God does not exist" is true (see note).
7. "God exists" is not true (from 3).
8. Therefore, "God does not exist" is true (from 6 and 7).

[NOTE]

Contradiction: If God exists is true, then God exists is not true.

Contradiction: If God does not exist is true, then God does not exist is not true.

Tautology: If God exists is true, then God does not exist is not true.

Equivalence (proving Atheist truth claim): If God exists is not true, then God does not exist is true.

Thus, by saying that "God exists" is not true, one is saying that "God does not exist" is true. It is a negative ontological truth claim that is inordinately difficult to support, which is why reasonable atheists avoid making such claims. It's not theistic sleight of hand; it's logical modus ponens.