Theorem bitru 1556

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 1551	. 2 ⊢ ⊤
3	1, 2	2th 265	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 207  ⊤wtru 1548

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 208  df-tru 1550

This theorem is referenced by:  truimtru  1570  falimtru  1572  falimfal  1573  notfal  1575  trubitru  1576  falbifal  1579  truorfal  1585  falortru  1586  exists1  2665  dfv2  3435  0frgp  19752  tgcgr4  28624  wl-2mintru1  37859  astbstanbst  47379  atnaiana  47393  dandysum2p2e4  47468