Metamath Proof Explorer


Theorem tru

Description: The truth value T. is provable. (Contributed by Anthony Hart, 13-Oct-2010)

Ref Expression
Assertion tru ⊢ ⊤

Proof

Step Hyp Ref Expression
1 id ⊢ ∀ x x = x → ∀ x x = x
2 df-tru ⊢ ⊤ ↔ ∀ x x = x → ∀ x x = x
3 1 2 mpbir ⊢ ⊤