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I was reading this question and one of the answers talked about Null Quantification, particularly it said that if $\varphi$ is a wff that does not contain $x$ as a free variable then:

$\forall x \varphi \Leftrightarrow \varphi$

I know that this seems trivial, but is there a way to prove it? I tried to but was unable. My main concern when attempting a proof is that the order in which the quantifiers are placed is important. Any light shed would be much appreciated.

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