Isomorphism theorems (groups/rings/modules)

First: G/ker φ ≅ im φ for any homomorphism φ. Second: (HN)/N ≅ H/(H∩N) when N normal. Third: (G/N)/(K/N) ≅ G/K when N ⊆ K, both normal. Formalises the quotient/substructure interplay.