apply phi_ih
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u (binders ∪ {x}) phi
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∪ {x}