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Definition df-coll 40880
Description: Define the collection operation. This is similar to the image set operation , but it uses Scott's trick to ensure the output is always a set. (Contributed by Rohan Ridenour, 11-Aug-2023.)
Assertion
Ref Expression
df-coll (𝐹 Coll 𝐴) = 𝑥𝐴 Scott (𝐹 “ {𝑥})
Distinct variable groups:   𝑥,𝐹   𝑥,𝐴

Detailed syntax breakdown of Definition df-coll
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cF . . 3 class 𝐹
31, 2ccoll 40879 . 2 class (𝐹 Coll 𝐴)
4 vx . . 3 setvar 𝑥
54cv 1537 . . . . . 6 class 𝑥
65csn 4551 . . . . 5 class {𝑥}
72, 6cima 5546 . . . 4 class (𝐹 “ {𝑥})
87cscott 40864 . . 3 class Scott (𝐹 “ {𝑥})
94, 1, 8ciun 4906 . 2 class 𝑥𝐴 Scott (𝐹 “ {𝑥})
103, 9wceq 1538 1 wff (𝐹 Coll 𝐴) = 𝑥𝐴 Scott (𝐹 “ {𝑥})
Colors of variables: wff setvar class
This definition is referenced by:  dfcoll2  40881  colleq12d  40882  nfcoll  40885  collexd  40886
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