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 ) )