Why does ~p ∧ q get replaced with F in this proof?

[mohabitar]

Everything in here makes sense up and till the last part, where they substituted (I think) F in for ~p ^ q, and then just ignored it and made it equivalent to the last part? Hope I'm not being too vague here.

 

[Dick]

They observed that ((not p) and p) is always false (F). Then they used that (false or anything)=anything. Is it the 'F' that throwing you off?

 

[mohabitar]

Oh ok I see so false and anything is always anything. That makes sense. So the F represents a substitution of the previous part but is also used to symbolize false, correct?

 

[Dick]

Oh ok I see so false and anything is always anything. That makes sense. So the F represents a substitution of the previous part but is also used to symbolize false, correct?

F=false. Presumably they would write T=true. And (false and anything)=false, that's not what they used. (false or anything)=anything.