Quantifiers - does this order matter?

[gmmstr827]

Is saying $\exists$x, $\exists$y
the same as saying $\exists$y, $\exists$x?

 

[micromass]

Hi gmmstr827!

No, in this case, the order doesn't matter.

 

[gmmstr827]

Alright, because the professor I have right now thinks those are two completely different things. He reads it as "there exists an x such that there exists a y (for that specific x)." This is the second time I had the class (it didn't transfer colleges) and my previous professor said they're the same thing.

Is there a law describing this somewhere?