# Modus Ponendo Ponens/Also known as

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## 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:

*... 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 "$\vdash \paren {p \supset q}$" and "$\vdash q$."

Remember that 1910: Alfred North Whitehead and Bertrand Russell: *Principia Mathematica* use $\supset$ to denote the implication function.

## Sources

- 1910: Alfred North Whitehead and Bertrand Russell:
*Principia Mathematica: Volume $\text { 1 }$*... (previous) ... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations - 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $3$: The Method of Deduction: $3.1$: Formal Proof of Validity: Rules of Inference: $1.$