Metamathematics I Problem Set 3

Due Monday October 1

1) Show that ϕ ⊢ ¬¬ϕ is derivable.

2) Show that the following version of the contrapostion inference rule is derivable.

\frac{Γ, ¬ϕ ⊢ ψ}{Γ, ¬ψ ⊢ ϕ}

3) Show that the following inference rule is derivable.

\frac{Γ ⊢ ∀xϕ}{Γ ⊢ ϕ}