Help with Logical Notation

Dear All.

I was hoping someone could give me a hand with expressing a couple of statements in terms of logical notation. I’m looking at verse 3 of the Gospel of John, which (for the present purposes) can be understood as follows:

John 1.3:3a: All (made) things came into being through the Word,

3b: and apart from the Word nothing came into being which has come into being.

I’d like to represent these statements logically. Something like:

Let X = the set of all made things,

and let P(x) = ‘x came into being by the Word’

Then 3a can be expressed as ? x ? X: P(x)

And 3b can be expressed as ¬ (? x ? X: ¬P(x))

But I doubt I’ve written these right. It’s a long time since I did anything like this.

Thanks in advance,

James.