The given definition of magma is:

df-mgm |- Mgm = { g | [. ( Base ` g ) / b ]. [. ( +g ` g ) / o ]. A. x e. b 
A. y e. b ( x o y ) e. b }


Would it be ok to define magma as follows:

df-mgm  |-  Mgm = { g | A. x e. ( Base ` g ) A. y e. ( Base ` g ) ( x ( +g 
` g ) y ) e. ( Base ` g ) }

If so, what problems would result ?

In other words, why was the given definition chosen over the more explicit 
definition ?

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