Theorem bitru 1365

Description: A theorem is equivalent to truth. (Contributed by Mario Carneiro, 9-May-2015.)

Hypothesis

Ref	Expression
bitru.1	|- ph

Assertion

Ref	Expression
bitru	|- ( ph <-> T. )

Proof of Theorem bitru

Step	Hyp	Ref	Expression
1		bitru.1	. 2 |- ph
2		tru 1357	. 2 |- T.
3	1, 2	2th 174	1 |- ( ph <-> T. )

Syntax hints:   <-> wb 105   T. wtru 1354

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 1356

This theorem is referenced by:  truorfal  1406  falortru  1407  truimtru  1409  falimtru  1411  falimfal  1412  notfal  1414  trubitru  1415  falbifal  1418