El axioma de Sustitución

x ∈ a y ∈ b
a b a∩b = ∅
a ⊔ b a a ⊔ b
α x α × {x}
(ζ, x) ≤ (η, x) ζ ≤ η ζ η
α ζ ↦→ (ζ, x)
α α × {x} α β
α × {0} β × {1} α
β
α β α β
α ⊕ β α × {0} ⊔ β × {1}
a b a ∼ α
b ∼ β a ⊔ b ∼ α × {0} ⊔ β × {1} α ⊕ β
α β
α β γ
0 ⊕ α = α ⊕ 0 = α
α ⊕ (β ⊕ γ) = (α ⊕ β) ⊕ γ
α ⊕ 1 = α ′
α ⊕ β ′ = (α ⊕ β) ′
0 × {0} ⊔ α × {1} = ∅ ⊔ α × {1} ∼
α ∼ α × {0} ⊔ ∅ = α × {0} ⊔ ∅ × {0}
a b c
〈x, 〈y, z〉〉 ↦→ 〈〈x, y〉, z〉
a ⊔ (b ⊔ c) (a ⊔ b) ⊔ c
f : α ′ ↦→ (α×{0}) ⊔ (1×{1}) f(ζ) =
α ⊕ β ′ = α ⊕ (β ⊕ 1) = (α ⊕ β) ⊕ 1 = (α ⊕ β) ′
(ζ, 0) ζ ∈ α
(0, 1) ζ = α