constructor
V : Type ?u.5314
inst✝ : SetTheory V
α : Sort u_1
p : α → Prop
⊢ (¬∀ (x : α), p x) ↔ ∃ x, ¬p x
case mp
V : Type ?u.5314
inst✝ : SetTheory V
α : Sort u_1
p : α → Prop
⊢ (¬∀ (x : α), p x) → ∃ x, ¬p x

case mpr
V : Type ?u.5314
inst✝ : SetTheory V
α : Sort u_1
p : α → Prop
⊢ (∃ x, ¬p x) → ¬∀ (x : α), p x