Theorem bitru 1360

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 1352	. 2 ⊢ ⊤
3	1, 2	2th 173	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 104  ⊤wtru 1349

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 1351

This theorem is referenced by:  truorfal  1401  falortru  1402  truimtru  1404  falimtru  1406  falimfal  1407  notfal  1409  trubitru  1410  falbifal  1413