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Definition df-tru 1440
Description: Definition of the truth value "true", or "verum", denoted by T.. This is a tautology, as proved by tru 1441. In this definition, an instance of id 22 is used as the definiens, although any tautology, such as an axiom, can be used in its place. This particular id 22 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 1441, and other proofs should depend on tru 1441 (directly or indirectly) instead of this definition, since there are many alternative 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 1438 . 2  wff T.
2 vx.tru . . . . . 6  setvar  x
32cv 1436 . . . . 5  class  x
43, 3wceq 1437 . . . 4  wff  x  =  x
54, 2wal 1435 . . 3  wff  A. x  x  =  x
65, 5wi 4 . 2  wff  ( A. x  x  =  x  ->  A. x  x  =  x )
71, 6wb 187 1  wff  ( T.  <-> 
( A. x  x  =  x  ->  A. x  x  =  x )
)
Colors of variables: wff setvar class
This definition is referenced by:  tru  1441
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