Theorem bitru 1296

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 1288	. 2 ⊢ ⊤
3	1, 2	2th 172	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 103  ⊤wtru 1285

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-tru 1287

This theorem is referenced by:  truorfal  1337  falortru  1338  truimtru  1340  falimtru  1342  falimfal  1343  notfal  1345  trubitru  1346  falbifal  1349