Today while day dreaming I discovered something interesting. I can prove a=a.(adsbygoogle = window.adsbygoogle || []).push({});

Here's how:

You can prove P=>P using natural deduction rules.(=> Intro)

So you can prove that x is an element of a => x is an element of a

Hence a is subset of a, and vice versa.

By ZFC axiom of extension, a=a

So a=a need not be an axiom, because it can be proven. In this sense, equality is not the fundamental concept. Set membership is.

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# Proof that a=a

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