Prove $\neg\exists x \neg P(x)$ is a logical consequence of $\forall x P(x)$

Question

How would you prove that 2. is a logical consequence of 1. using a Fitch style proof?

1. $\forall x P(x)$

2. $\neg\exists x \neg P(x)$

Answer 1

This was done using Fitch. You need to start first by assuming that what you want to prove is false. From here you can perform existential elimination, which will eventually entail a contradiction. This will then allow you to reject your assumption, thus proving your conclusion.