Theorem bitru 1550

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 1545	. 2 ⊢ ⊤
3	1, 2	2th 263	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 205  ⊤wtru 1542

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 1544

This theorem is referenced by:  truimtru  1564  falimtru  1566  falimfal  1567  notfal  1569  trubitru  1570  falbifal  1573  truorfal  1579  falortru  1580  exists1  2655  dfv2  3449  0frgp  19575  tgcgr4  27536  wl-2mintru1  36034  astbstanbst  45264  atnaiana  45278  dandysum2p2e4  45353