Definition df-tru 1367

Description: Definition of the truth value "true", or "verum", denoted by T.. This is a tautology, as proved by tru 1368. 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 1368, and other proofs should depend on tru 1368 (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

Step	Hyp	Ref	Expression
1		wtru 1365	. 2 wff T.
2		vx.tru	. . . . . 6 setvar x
3	2	cv 1363	. . . . 5 class x
4	3, 3	wceq 1364	. . . 4 wff x = x
5	4, 2	wal 1362	. . 3 wff A. x x = x
6	5, 5	wi 4	. 2 wff ( A. x x = x -> A. x x = x )
7	1, 6	wb 105	1 wff ( T. <-> ( A. x x = x -> A. x x = x ) )

This definition is referenced by:  tru  1368