Factoring Quantifiers

-For:

• Quantifier $Q$
• Logical Predicate $E$ Then:

1. $E\wedge QxF\equiv Qx(E\wedge F)$ if $x$ is not Free Predicate Variable in $E$
2. $E\vee QxF\equiv Qx(E\vee F)$ if $x$ is not Free Predicate Variable in $E$
3. $QxE\wedge F\equiv Qx(E\wedge F)$ if $x$ is not Free Predicate Variable in $F$
4. $QxE\vee F\equiv Qx(E\vee F)$ if $x$ is not Free Predicate Variable in $F$
5. $QxE\to F\equiv \overline{Q}x(E\to F)$ if $x$ is not Free Predicate Variable in $F$
6. $E\to QxF\equiv Qx(E\to F)$ if $x$ is not Free Predicate Variable in $E$