Symmetric Groups of Same Order are Isomorphic/Proof 1

Proof
Consider the symmetric group on $n$ letters $S_n$.

From Symmetric Group on n Letters is Isomorphic to Symmetric Group we have that:


 * $\struct {\map \Gamma {T_1}, \circ}$ is isomorphic to $S_n$


 * $\struct {\map \Gamma {T_2}, \circ}$ is isomorphic to $S_n$

and hence from Isomorphism is Equivalence Relation:


 * $\struct {\map \Gamma {T_1}, \circ}$ is isomorphic to $\struct {\map \Gamma {T_2}, \circ}$.