ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-tru Unicode version

Definition df-tru 1345
Description: Definition of the truth value "true", or "verum", denoted by T.. This is a tautology, as proved by tru 1346. In this definition, an instance of id 19 is used as the definiens, although any tautology, such as an axiom, can be used in its place. This particular id 19 instance was chosen so this definition can be checked by the same algorithm that is used for predicate calculus. This definition should be referenced directly only by tru 1346, and other proofs should depend on tru 1346 (directly or indirectly) instead of this definition, since there are many alternate ways to define T.. (Contributed by Anthony Hart, 13-Oct-2010.) (Revised by NM, 11-Jul-2019.) (New usage is discouraged.)
Assertion
Ref Expression
df-tru  |-  ( T.  <-> 
( A. x  x  =  x  ->  A. x  x  =  x )
)

Detailed syntax breakdown of Definition df-tru
StepHypRef Expression
1 wtru 1343 . 2  wff T.
2 vx.tru . . . . . 6  setvar  x
32cv 1341 . . . . 5  class  x
43, 3wceq 1342 . . . 4  wff  x  =  x
54, 2wal 1340 . . 3  wff  A. x  x  =  x
65, 5wi 4 . 2  wff  ( A. x  x  =  x  ->  A. x  x  =  x )
71, 6wb 104 1  wff  ( T.  <-> 
( A. x  x  =  x  ->  A. x  x  =  x )
)
Colors of variables: wff set class
This definition is referenced by:  tru  1346
  Copyright terms: Public domain W3C validator