Theorem bitru 1572

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 1567	. 2 ⊢ ⊤
3	1, 2	2th 267	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 209  ⊤wtru 1564

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 210  df-tru 1566

This theorem is referenced by:  truimtru  1586  falimtru  1588  falimfal  1589  notfal  1591  trubitru  1592  falbifal  1595  truorfal  1601  falortru  1602  exists1  2690  dfv2  3460  0frgp  19840  tgcgr4  28758  wl-2mintru1  37996  astbstanbst  47501  atnaiana  47515  dandysum2p2e4  47590