Definition:Interderivable

If two statements $$p$$ and $$q$$ are such that:


 * $$p \vdash q$$, i.e. $$p$$ therefore $$q$$
 * $$q \vdash p$$, i.e. $$q$$ therefore $$p$$

then $$p$$ and $$q$$ are said to be interderivable.

$$p \dashv \vdash q$$ means "$$p \vdash q \ \mathbf {and} \ q \vdash p$$".

Note that because the conclusion of an argument is a single statement, there can be only one statement on either side of the $$\dashv \vdash$$ sign.