Propositional Logic: Validity of sequent $\lnot\Phi_1 \land \lnot \Phi_2 \vdash \Phi_1 \rightarrow \Phi_2$
- $\lnot \Phi_1 \land \lnot \Phi_2$ (premise)
- $\Phi_1$ (assumption)
- $\lnot \Phi_1$ ($\land e_1$) 1
- $\bot$ ($\lnot e$) 2,3
$\Phi_2$ ($\bot e$) 4
$\Phi_1 \rightarrow \Phi_2$ ($\rightarrow i$) 2,5
All this look really weird to me. I work with $\Phi_1$ and $\lnot \Phi_1$ at the same time.
Can someone tell me how to proceed and why this is valid?
Taken from the book "Logic in Computer Science" by Michael Huth and Mark Ryan.