let F := forall_ x phi
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))