Proposition 6

Let E and F be two magmas and f a homomorphism of E into F. Let R[x, y] denote the relation f(x) = f(y) between elements x, y of E. Then R is an equivalence relation on E compatible with the law on E and the mapping of E/R onto f(E) derived from f by passing to the quotient is an isomorphism of the quotient magma E/R onto the submagma f(E) of F.