Theorem bitru 1546

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 1541	. 2 ⊢ ⊤
3	1, 2	2th 266	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 208  ⊤wtru 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-tru 1540

This theorem is referenced by:  truimtru  1560  falimtru  1562  falimfal  1563  notfal  1565  trubitru  1566  falbifal  1569  truorfal  1575  falortru  1576  exists1  2746  0frgp  18905  tgcgr4  26317  astbstanbst  43165  atnaiana  43179  dandysum2p2e4  43254