quantifier equivalences

[evagelos]

prove the following equivalences:

1)\neg\forall x\neg Fx\Longleftrightarrow\exists xFx

2)\neg\forall x Fx\Longleftrightarrow\exists x\neg Fx

By using the 4 quantifier laws:

1) Universal Elimination

2) Universal Introduction

3)Existential Introduction

4)Existential Elimination

And the laws of propositional calculus