# Modus Ponendo Ponens/Also known as

## Proof Rule

Modus Ponendo Ponens is also known as:

• Modus ponens, abbreviated M.P.
• The rule of implies-elimination
• The rule of arrow-elimination
• The rule of (material) detachment
• The process of inference

1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica: Volume $\text { 1 }$, 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:

"$\vdash p \supset \, \vdash q$,"
"$\vdash p$" and "$\vdash \paren {p \supset q}$" and "$\vdash q$."
Remember that 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica use $\supset$ to denote the implication function.