Construct a formal logical proof using predicate logic symbols to demonstrate the validity of the following argument: 'All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.' Explicitly define your predicates (e.g., H(x) for 'x is a human', M(x) for 'x is mortal') and show the derivation step-by-step using rules of inference like Universal Instantiation and Modus Ponens.