Theorem bitru 1568

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 1563	. 2 ⊢ ⊤
3	1, 2	2th 266	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 208  ⊤wtru 1560

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 1562

This theorem is referenced by:  truimtru  1582  falimtru  1584  falimfal  1585  notfal  1587  trubitru  1588  falbifal  1591  truorfal  1597  falortru  1598  exists1  2686  dfv2  3456  0frgp  19802  tgcgr4  28677  wl-2mintru1  37948  astbstanbst  47467  atnaiana  47481  dandysum2p2e4  47556