Theorem prodeq1

Description: Equality theorem for a product. (Contributed by Scott Fenton, 1-Dec-2017)

	Ref	Expression
Assertion	prodeq1	⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		nfcv	⊢ Ⅎ 𝑘 𝐴
2		nfcv	⊢ Ⅎ 𝑘 𝐵
3	1 2	prodeq1f	⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 )