The definition of a faithful right group action on itself is
For any two distinct g_1 and g_2 in G (g_1 \neq g_2), there exists h in G such that h^{g_1} \neq h^{g_2}.
The contrapositive of the above is
If h^{g_1} = h^{g_2} for all h in G, then g_1 = g_2.
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