Modus Ponendo Ponens/Also known as

Proof Rule
Modus Ponendo Ponens is also known as:


 * Modus ponens
 * The rule of implies-elimination
 * The rule of arrow-elimination
 * The rule of (material) detachment
 * The process of inference

, seemingly uneasy with the language they are using, state:
 * The process of the inference cannot be reduced to symbols.

Having said that, they then go on to write:
 * ''... we shall write instead
 * "$\vdash p \supset \, \vdash q$,"
 * which is to be considered as a mere abbreviation of the threefold statement
 * "$\vdash p$" and "$\vdash \left({p \supset q}\right)$" and "$\vdash q$."

Remember that use $\supset$ to denote the implication function.