I often encountered (when discussing politics, theology or similar subjective topics) a fallacy which is similar to this one, or maybe it can be seen as the reverse of it.

• A: ice is hot, therefore 2+2=4
• B: No, ice is not hot, but even if it was, it still wouldn't be a good proof for 2+2=4
• A: So you don't believe in the obvious truth that 2+2=4 ?

Also, sometimes A might try to prove 2+2=5 with the same strategy.