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micromass
#7
Aug13-11, 06:53 PM
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When you take G the equality, then your list of axioms is that of a commutative group. The thing you need to prove is that the identity element is unique.

Take two identity's c and c', then

3) G(F(c',c),c')

and

3) G(F(c,c'),c)

and

4) G(F(c,c'),F(c',c))

So by (5), we get that G(c,c')

But that doesn't give equality, however...