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Definition df-tru 1627
 Description: Definition of the truth value "true", or "verum", denoted by ⊤. This is a tautology, as proved by tru 1628. 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 1628, and other proofs should depend on tru 1628 (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 1628 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 1625 . 2 wff
2 vx.tru . . . . . 6 setvar 𝑥
32cv 1623 . . . . 5 class 𝑥
43, 3wceq 1624 . . . 4 wff 𝑥 = 𝑥
54, 2wal 1622 . . 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  1628
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