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Definition df-tru 1526
Description: Definition of the truth value "true", or "verum", denoted by . This is a tautology, as proved by tru 1527. 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 1527, and other proofs should depend on tru 1527 (directly or indirectly) instead of this definition, since there are many alternate ways to define . (Contributed by Anthony Hart, 13-Oct-2010.) (Revised by NM, 11-Jul-2019.) Use tru 1527 instead. (New usage is discouraged.)
Assertion
Ref Expression
df-tru (⊤ ↔ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))

Detailed syntax breakdown of Definition df-tru
StepHypRef Expression
1 wtru 1524 . 2 wff
2 vx.tru . . . . . 6 setvar 𝑥
32cv 1522 . . . . 5 class 𝑥
43, 3wceq 1523 . . . 4 wff 𝑥 = 𝑥
54, 2wal 1521 . . 3 wff 𝑥 𝑥 = 𝑥
65, 5wi 4 . 2 wff (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥)
71, 6wb 196 1 wff (⊤ ↔ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  tru  1527
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