Commutativity of intersection
From Maths
[math]A\cap B=B\cap A[/math]
TODO:
Note
This is somewhere between a theorem and a definition because at some point you have to accept "and" is commutative or something.
Proof
[math]\implies[/math]
[math]x\in A\cap B\implies x\in A\text{ and }x\in B\implies x\in B\text{ and }x\in A\implies x\in B\cap A[/math], thus by the implies and subset relation we see [math]A\cap B\subset B\cap A[/math]
[math]\impliedby[/math]
By the exact same procedure we see [math]B\cap A\subset A\cap B[/math]
Thus we conclude [math]A\cap B=B\cap A[/math]
Set Theory
