a deductive argument form and rule of inference

C \to can be shown that with only these three axiom schemata and '' modus ponens In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for 'method of putting by placing') or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference.

an inference rule that allows us to deduce new propositions from old ones

The difference is that this tautology is a single proposition, whereas modus ponens is an inference rule that allows us to deduce new propositions from old ones.

a form of valid inference

Modus Ponens (Latin: mode that affirms; often abbreviated as MP) is a form of valid inference.

a famous rule of logic

Modus ponens is a famous rule of logic used in natural deduction.

as modus ponendo ponens (Latin for 'method of putting by placing') or or , implication elimination affirming the antecedent

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (Latin for 'method of putting by placing') or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference.

method of affirming

In contrast, the Latin term “modus ponens” means “method of affirming.”

as modus ponendo ponens (Latin for 'method of putting by placing'),[1] implication elimination, or affirming the antecedent,[2

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'),[1] implication elimination, or affirming the antecedent,[2] is a deductive argument form and rule of inference.[3]