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Definition df-scott 40878
Description: Define the Scott operation. This operation constructs a subset of the input class which is nonempty whenever its input is using Scott's trick. (Contributed by Rohan Ridenour, 9-Aug-2023.)
Assertion
Ref Expression
df-scott Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
Distinct variable group:   𝑥,𝑦,𝐴

Detailed syntax breakdown of Definition df-scott
StepHypRef Expression
1 cA . . 3 class 𝐴
21cscott 40877 . 2 class Scott 𝐴
3 vx . . . . . . 7 setvar 𝑥
43cv 1537 . . . . . 6 class 𝑥
5 crnk 9180 . . . . . 6 class rank
64, 5cfv 6334 . . . . 5 class (rank‘𝑥)
7 vy . . . . . . 7 setvar 𝑦
87cv 1537 . . . . . 6 class 𝑦
98, 5cfv 6334 . . . . 5 class (rank‘𝑦)
106, 9wss 3908 . . . 4 wff (rank‘𝑥) ⊆ (rank‘𝑦)
1110, 7, 1wral 3130 . . 3 wff 𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)
1211, 3, 1crab 3134 . 2 class {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
132, 12wceq 1538 1 wff Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
Colors of variables: wff setvar class
This definition is referenced by:  scotteqd  40879  nfscott  40881  scottabf  40882  scottss  40885  scottex2  40887  scotteld  40888  scottelrankd  40889
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