x = y → y = y
T → x = y → y = y
∀ (x_1 : T), x = x_1 → x_1 = y
∀ (x_1 : T), x_1 = x → x = x
T → T → x = y → y = y
T → T → x = y → P y
(∀ (x : T), P x ↔ Q x) → Q x
Prop → (∀ (x : T), P x ↔ Q x) → Prop → Q x
∀ (x_1 : Prop), (∀ (x : T), P x ↔ Q x) → x_1 ∨ Q x
(∀ (x : T), P x ↔ Q x) → Q x
∀ (x : T), T → (∀ (x : T), P x ↔ Q x) → Q x
∀ (x x_1 : T), x = x_1 → P x_1
∀ (x x_1 x_2 : T), x = x_1 → x_1 = x_2 → P x_2
∀ (x x_1 : T), x = x_1 → (∀ (w : T), P w ↔ Q w) → Q x_1