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 ) )