Theorem bitru 1343

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

Hypothesis

Ref	Expression
bitru.1	⊢ 𝜑

Assertion

Ref	Expression
bitru	⊢ (𝜑 ↔ ⊤)

Proof of Theorem bitru

Step	Hyp	Ref	Expression
1		bitru.1	. 2 ⊢ 𝜑
2		tru 1335	. 2 ⊢ ⊤
3	1, 2	2th 173	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 104  ⊤wtru 1332

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-tru 1334

This theorem is referenced by:  truorfal  1384  falortru  1385  truimtru  1387  falimtru  1389  falimfal  1390  notfal  1392  trubitru  1393  falbifal  1396