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Definition df-wlimOLD 31003
Description: Define the class of limit points of a well-founded set. (Contributed by Scott Fenton, 15-Jun-2018.) Obsolete version of df-wlim 31002 as of 10-Oct-2021. (New usage is discouraged.)
Assertion
Ref Expression
df-wlimOLD WLimOLD(𝑅, 𝐴) = {𝑥𝐴 ∣ (𝑥 ≠ sup(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))}
Distinct variable groups:   𝑥,𝑅   𝑥,𝐴

Detailed syntax breakdown of Definition df-wlimOLD
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
31, 2cwlimOLD 30999 . 2 class WLimOLD(𝑅, 𝐴)
4 vx . . . . . 6 setvar 𝑥
54cv 1474 . . . . 5 class 𝑥
62ccnv 5037 . . . . . 6 class 𝑅
71, 1, 6csup 8229 . . . . 5 class sup(𝐴, 𝐴, 𝑅)
85, 7wne 2780 . . . 4 wff 𝑥 ≠ sup(𝐴, 𝐴, 𝑅)
91, 2, 5cpred 5596 . . . . . 6 class Pred(𝑅, 𝐴, 𝑥)
109, 1, 2csup 8229 . . . . 5 class sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅)
115, 10wceq 1475 . . . 4 wff 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅)
128, 11wa 383 . . 3 wff (𝑥 ≠ sup(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))
1312, 4, 1crab 2900 . 2 class {𝑥𝐴 ∣ (𝑥 ≠ sup(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))}
143, 13wceq 1475 1 wff WLimOLD(𝑅, 𝐴) = {𝑥𝐴 ∣ (𝑥 ≠ sup(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))}
Colors of variables: wff setvar class
This definition is referenced by:  elwlimOLD  31014
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