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Definition df-tru 1546
Description: Definition of the truth value "true", or "verum", denoted by . 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 instance of id 22 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 1547, and other proofs should use tru 1547 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 1547 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 1544 . 2 wff
2 vx.tru . . . . . 6 setvar 𝑥
32cv 1542 . . . . 5 class 𝑥
43, 3wceq 1543 . . . 4 wff 𝑥 = 𝑥
54, 2wal 1541 . . 3 wff 𝑥 𝑥 = 𝑥
65, 5wi 4 . 2 wff (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥)
71, 6wb 209 1 wff (⊤ ↔ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  tru  1547
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