Metamath Proof Explorer


Theorem bitru

Description: A theorem is equivalent to truth. (Contributed by Mario Carneiro, 9-May-2015)

Ref Expression
Hypothesis bitru.1 ⊢ φ
Assertion bitru ⊢ φ ↔ ⊤

Proof

Step Hyp Ref Expression
1 bitru.1 ⊢ φ
2 tru ⊢ ⊤
3 1 2 2th ⊢ φ ↔ ⊤