Theorem bitru 1551

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 1546	. 2 ⊢ ⊤
3	1, 2	2th 264	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 205  ⊤wtru 1543

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 206  df-tru 1545

This theorem is referenced by:  truimtru  1565  falimtru  1567  falimfal  1568  notfal  1570  trubitru  1571  falbifal  1574  truorfal  1580  falortru  1581  exists1  2657  dfv2  3478  0frgp  19640  tgcgr4  27762  wl-2mintru1  36309  astbstanbst  45554  atnaiana  45568  dandysum2p2e4  45643