Evidence for atheism

[Angrboda]

The following invalid argument in natural language:

If a, b;
c;
therefore b.

is represented sententially as:

((( a ⇒ b) Λ (c)) ⇒ b )

This statement as a whole is false; we can conclude nothing about (b) as an independent proposition. Moreover, we can use this sentence as a whole in another proposition in place of the value FALSE and order is preserved, and any argument based on that is valid and sound with respect to this part of the syllogism, no matter how we transform the original statement via the laws of logic. However, substituting b for FALSE is not an order preserving operation and any arguments formed from doing so are for that reason invalid and result in a non sequitur.