Theorem bitru 1255

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 1247	. 2 ⊢ ⊤
3	1, 2	2th 163	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 98  ⊤wtru 1244

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-tru 1246

This theorem is referenced by:  truorfal  1297  falortru  1298  truimtru  1300  falimtru  1302  falimfal  1303  notfal  1305  trubitru  1306  falbifal  1309