Theorem bitru 1311

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 1303	. 2 ⊢ ⊤
3	1, 2	2th 173	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 104  ⊤wtru 1300

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

This theorem depends on definitions:  df-bi 116  df-tru 1302

This theorem is referenced by:  truorfal  1352  falortru  1353  truimtru  1355  falimtru  1357  falimfal  1358  notfal  1360  trubitru  1361  falbifal  1364