Theorem bitru 1409

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 1401	. 2 ⊢ ⊤
3	1, 2	2th 174	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 105  ⊤wtru 1398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-tru 1400

This theorem is referenced by:  truorfal  1450  falortru  1451  truimtru  1453  falimtru  1455  falimfal  1456  notfal  1458  trubitru  1459  falbifal  1462