Transformation rules 

Propositional calculus 
Rules of inference 
Rules of replacement 
Predicate logic 
In propositional logic, tautology is either of two commonly used rules of replacement.^{[1]}^{[2]}^{[3]} The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:
The principle of idempotency of disjunction:
and the principle of idempotency of conjunction:
Where "" is a metalogical symbol representing "can be replaced in a logical proof with."
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Logic Lesson 6: Proofs with the Rules of Inference

Proving a compound proposition is a tautology part 2 of 2

CS101  Discrete Mathematics  Rules of Inference (রুলস অব ইনফারেন্স)
Transcription
Formal notation
Theorems are those logical formulas where is the conclusion of a valid proof,^{[4]} while the equivalent semantic consequence indicates a tautology.
The tautology rule may be expressed as a sequent:
and
where is a metalogical symbol meaning that is a syntactic consequence of , in the one case, in the other, in some logical system;
or as a rule of inference:
and
where the rule is that wherever an instance of "" or "" appears on a line of a proof, it can be replaced with "";
or as the statement of a truthfunctional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:
and
where is a proposition expressed in some formal system.
References
 ^ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. pp. 364–5.
 ^ Copi and Cohen
 ^ Moore and Parker
 ^ Logic in Computer Science, p. 13