Theorem colleq2

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

	Ref	Expression
Assertion	colleq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 Coll 𝐴 ) = ( 𝐹 Coll 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		eqidd	⊢ ( 𝐴 = 𝐵 → 𝐹 = 𝐹 )
2		id	⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
3	1 2	colleq12d	⊢ ( 𝐴 = 𝐵 → ( 𝐹 Coll 𝐴 ) = ( 𝐹 Coll 𝐵 ) )