One Notational Shorthand

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Subsection 4.2.5 One Notational Shorthand

Now that we understand when we have to be careful about the way that we write quantified expressions, we will extend our syntax slightly just to make common things less cumbersome. When we have several of the same quantifier in a row, we can collapse them like this:

∀x (∀y (∀z (P(x, y, z)))) can be rewritten as ∀x, y, z (P(x, y, z))

And similarly for ∃:

∃x (∃y (∃z (P(x, y, z)))) can be rewritten as ∃x, y, z (P(x, y, z))