MHB How to Prove Predicate Logic Validity with Induction?

[Voehet]

How would I go about proving that the argument below is valid using the induction method?
(∃x)[P(x)!Q(x)]^(∀y)[Q(y)!R(y)]^(∀x)P(x)!(∃x)R(x)

Thank you very much in advance!

 

[MarkFL]

Hello and welcome to MHB, Voehet! :D

We ask that our users show their progress when posting questions, and that way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[Evgeny.Makarov]

How would I go about proving that the argument below is valid using the induction method?
(∃x)[P(x)!Q(x)]^(∀y)[Q(y)!R(y)]^(∀x)P(x)!(∃x)R(x)

What does ! stand for?