Theorem bitru 1549

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 1544	. 2 ⊢ ⊤
3	1, 2	2th 264	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 206  ⊤wtru 1541

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 207  df-tru 1543

This theorem is referenced by:  truimtru  1563  falimtru  1565  falimfal  1566  notfal  1568  trubitru  1569  falbifal  1572  truorfal  1578  falortru  1579  exists1  2661  dfv2  3483  0frgp  19797  tgcgr4  28539  wl-2mintru1  37491  astbstanbst  46921  atnaiana  46935  dandysum2p2e4  47010