Sentence:  The proof that isomorphism is an equivalence relation relies on three fundamental properties of <WSD>bijective</WSD> functions (functions that are one-to-one and onto): (1) every identity function is <WSD>bijective</WSD>, (2) the inverse of every <WSD>bijective</WSD> function is also <WSD>bijective</WSD>, (3) the composition of two <WSD>bijective</WSD> functions is <WSD>bijective</WSD>. 
Meaning of the word marked with <WSD> tags:  Both injective and surjective.