Theorem bitru 1326

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 1321	. 2 ⊢ ⊤
3	1, 2	2th 230	1 ⊢ (φ ↔ ⊤ )

This proof depends on syntax axioms:   ↔ wb 176   ⊤ wtru 1316

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-tru 1319

This theorem is used by:  truorfal  1341  falortru  1342  truimtru  1344  falimtru  1346  falimfal  1347  notfal  1349  trubitru  1350  falbifal  1353