have := pI_prop.2.2
case h.right.right
φ ψ : Formula
hyp : φ⊨ψ
X : TNode := ([φ], [~ψ], none)
ctX : ClosedTableau ([], []) X
θ : Formula
pI_prop : voc θ ⊆ jvoc X ∧ ¬satisfiable ((~θ) :: X.left) ∧ ¬satisfiable (θ :: X.right)
⊢ θ⊨ψ
case h.right.right
φ ψ : Formula
hyp : φ⊨ψ
X : TNode := ([φ], [~ψ], none)
ctX : ClosedTableau ([], []) X
θ : Formula
pI_prop : voc θ ⊆ jvoc X ∧ ¬satisfiable ((~θ) :: X.left) ∧ ¬satisfiable (θ :: X.right)
this : ¬satisfiable (θ :: X.right)
⊢ θ⊨ψ