no goals
α : Type u
β : Type v
γ : Type ?u.47317
δ : Type ?u.47320
ε : Type ?u.47323
ζ : Type ?u.47326
inst✝⁵ : TopologicalSpace α
inst✝⁴ : TopologicalSpace β
inst✝³ : TopologicalSpace γ
inst✝² : TopologicalSpace δ
inst✝¹ : TopologicalSpace ε
inst✝ : TopologicalSpace ζ
s : Set (α × β)
⊢ (∀ (a : α × β), a ∈ s → s ∈ 𝓝 a) ↔
    ∀ (a : α) (b : β), (a, b) ∈ s → ∃ u v, IsOpen u ∧ IsOpen v ∧ a ∈ u ∧ b ∈ v ∧ u ×ˢ v ⊆ s
simp_rw [Prod.forall, mem_nhds_prod_iff', and_left_comm]