Hello everybody!

There are some special cases I need to know how to prove (and find it very difficult to find everywhere) using the

__standard logic identities__ and nothing very specific like axiomatized systems nor special normal forms like Skolem, etc.

First: how can I determine if the following implication is true or false?

(

x)[P(x)

Q(x)]

[

P(x)

Q(x)]

A book I have states that it is true, but it doesn't explain why. The exercise pretends the determination of its truth o falsity only using std logical identities like using the implication, the contrapositive, DeMorgan, etc. I also know that

only distributes over AND, and

only distributes over OR.

Thank you and hope you help me to construct this proof.