# Modus Ponendo Tollens/Proof Rule/Technical Note

## Technical Note on Modus Ponendo Tollens

When invoking Modus Ponendo Tollens in a tableau proof, use the {{ModusPonendoTollens}} template:

{{ModusPonendoTollens|line|pool|statement|first|second|1 or 2}}

or:

{{ModusPonendoTollens|line|pool|statement|first|second|1 or 2|comment}}

where:

line is the number of the line on the tableau proof where Modus Ponendo Tollens is to be invoked
pool is the pool of assumptions (comma-separated list)
statement is the statement of logic that is to be displayed in the Formula column, without the $...$ delimiters
first is the first of the two lines of the tableau proof upon which this line directly depends, the one in the form $\neg \left({\phi \land \psi}\right)$
second is the second of the two lines of the tableau proof upon which this line directly depends, the one in the form $\phi$ or $\psi$
1 or 2 should hold 1 for ModusPonendoTollens_1, and 2 for ModusPonendoTollens_2
comment is the (optional) comment that is to be displayed in the Notes column.