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Definition df-scott 42995
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 = {π‘₯ ∈ 𝐴 ∣ βˆ€π‘¦ ∈ 𝐴 (rankβ€˜π‘₯) βŠ† (rankβ€˜π‘¦)}
Distinct variable group:   π‘₯,𝑦,𝐴

Detailed syntax breakdown of Definition df-scott
StepHypRef Expression
1 cA . . 3 class 𝐴
21cscott 42994 . 2 class Scott 𝐴
3 vx . . . . . . 7 setvar π‘₯
43cv 1541 . . . . . 6 class π‘₯
5 crnk 9758 . . . . . 6 class rank
64, 5cfv 6544 . . . . 5 class (rankβ€˜π‘₯)
7 vy . . . . . . 7 setvar 𝑦
87cv 1541 . . . . . 6 class 𝑦
98, 5cfv 6544 . . . . 5 class (rankβ€˜π‘¦)
106, 9wss 3949 . . . 4 wff (rankβ€˜π‘₯) βŠ† (rankβ€˜π‘¦)
1110, 7, 1wral 3062 . . 3 wff βˆ€π‘¦ ∈ 𝐴 (rankβ€˜π‘₯) βŠ† (rankβ€˜π‘¦)
1211, 3, 1crab 3433 . 2 class {π‘₯ ∈ 𝐴 ∣ βˆ€π‘¦ ∈ 𝐴 (rankβ€˜π‘₯) βŠ† (rankβ€˜π‘¦)}
132, 12wceq 1542 1 wff Scott 𝐴 = {π‘₯ ∈ 𝐴 ∣ βˆ€π‘¦ ∈ 𝐴 (rankβ€˜π‘₯) βŠ† (rankβ€˜π‘¦)}
Colors of variables: wff setvar class
This definition is referenced by:  scotteqd  42996  nfscott  42998  scottabf  42999  scottss  43002  scottex2  43004  scotteld  43005  scottelrankd  43006
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