Tricky Logical Problem: Solving for \forallx\forally\existsz

[studas]

Homework Statement

This is a problem I have been had some troubles understanding in my Discrete Mathematics course.

[PLAIN]http://i.imgur.com/HTUNr7f.png[/PLAIN]


$\forall$x$\forall$y$\exists$z(x<z$\rightarrow$x≥y)

Homework Equations

I know that this statement is true, according to the solutions page, but I just cannot comprehend why?

The Attempt at a Solution

Does anyone have any ideas?

 

[csopi]

The statement is true, because if you choose z to be less or equal to x, then (x < z) is a false statement, so (x < z ) -> A is always true, regardless of "A".