Metamath Proof Explorer


Definition df-coll

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)

Ref Expression
Assertion df-coll ( 𝐹 Coll 𝐴 ) = 𝑥𝐴 Scott ( 𝐹 “ { 𝑥 } )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cF 𝐹
1 cA 𝐴
2 1 0 ccoll ( 𝐹 Coll 𝐴 )
3 vx 𝑥
4 3 cv 𝑥
5 4 csn { 𝑥 }
6 0 5 cima ( 𝐹 “ { 𝑥 } )
7 6 cscott Scott ( 𝐹 “ { 𝑥 } )
8 3 1 7 ciun 𝑥𝐴 Scott ( 𝐹 “ { 𝑥 } )
9 2 8 wceq ( 𝐹 Coll 𝐴 ) = 𝑥𝐴 Scott ( 𝐹 “ { 𝑥 } )