Theorem bitru 1548

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 1543	. 2 ⊢ ⊤
3	1, 2	2th 263	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 205  ⊤wtru 1540

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 1542

This theorem is referenced by:  truimtru  1562  falimtru  1564  falimfal  1565  notfal  1567  trubitru  1568  falbifal  1571  truorfal  1577  falortru  1578  exists1  2662  dfv2  3425  0frgp  19300  tgcgr4  26796  wl-2mintru1  35588  astbstanbst  44291  atnaiana  44305  dandysum2p2e4  44380