Propositional Inference Rules:

Propositional Inference Rules Equivalence rules are mostly useful because of the vice-versa aspect, that means like we can search backwards and forwards in a search space using them. Thus, we can perform bi-directional search, that is a bonus. Moreover, what if we know the one sentence or set of sentences that being true implies that another set of sentences is true. So just for instance here the following sentence is used ad nauseum in logic text books as: 

'All men are mortal'

'Socrates was a man'

Hence, 'Socrates is mortal' 

Above example is of the application of a rule of deduction which is called as Modus Ponens. Hence we considered that we have deduced the fact in which 'Socrates is mortal' from the two true facts i.e. 'all men are mortal' and 'Socrates was a man'. It means that we know the rule about men being mortal and the classification of Socrates as a man are true and we can infer with certainty is just because we know the cmodus ponens is sound in which Socrates is going to die - which, obviously, he did. Evidently, it doesn't make sense to go backwards as with equivalences: so we would deduce that, like Socrates being mortal implies here that he was a man so all men are mortal!!