Replacement rule

The replacement rule is a final rule of many logical calculi .

From the premises

P [A] (which means that the statement A is contained in the statement P)

${\displaystyle A\leftrightarrow B}$

follows the conclusion

P [B]

So - in terms of content - part of a statement is replaced by an equivalent one .

Example:

The premise is given . Because of the generality of can be the expression on the premise by replacing. ${\displaystyle (p\rightarrow q)\wedge p}$ ${\displaystyle (p\rightarrow q)\leftrightarrow (\neg p\vee q)}$ ${\displaystyle (p\rightarrow q)}$ ${\displaystyle (\neg p\vee q)}$

From the statement ${\displaystyle (p\rightarrow q)\wedge p}$

so follows ${\displaystyle (\neg p\vee q)\wedge p,}$

so ${\displaystyle (\neg p\wedge p)\vee (q\wedge p),}$

so ${\displaystyle (q\wedge p).}$

See also

• Final rule
• Insertion rule (logic)