x = y → true
T → x = y → true
∀ (a : T), x = a → a = y
∀ (a : T), a = x → true
T → T → x = y → true
T → T → x = y → P y
(∀ (x : T), P x ↔ Q x) → Q x
Prop → (∀ (x : T), P x ↔ Q x) → Prop → Q x
∀ (a : Prop), (∀ (x : T), P x ↔ Q x) → a ∨ Q x
(∀ (x : T), P x ↔ Q x) → Q x
∀ (a : T), T → (∀ (x : T), P x ↔ Q x) → Q a
∀ (a a_1 : T), a = a_1 → P a_1
∀ (a a_1 a_2 : T), a = a_1 → a_1 = a_2 → P a_2
∀ (a a_1 : T), a = a_1 → (∀ (w : T), P w ↔ Q w) → Q a_1