Theorem bitru 1496

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 1487	. 2 ⊢ ⊤
3	1, 2	2th 254	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 196  ⊤wtru 1484

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 197  df-tru 1486

This theorem is referenced by:  truorfal  1511  falortru  1512  truimtru  1514  falimtru  1516  falimfal  1517  notfal  1519  trubitru  1520  falbifal  1523  0frgp  18192  tgcgr4  25426  astbstanbst  41076  atnaiana  41090  dandysum2p2e4  41165