Metamath Proof Explorer


Theorem colleq1

Description: Equality theorem for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023)

Ref Expression
Assertion colleq1 F = G F Coll A = G Coll A

Proof

Step Hyp Ref Expression
1 id F = G F = G
2 eqidd F = G A = A
3 1 2 colleq12d F = G F Coll A = G Coll A