Theorem prodeq1i

Description: Equality inference for product. (Contributed by Scott Fenton, 4-Dec-2017)

	Ref	Expression
Hypothesis	prodeq1i.1	⊢ 𝐴 = 𝐵
Assertion	prodeq1i	⊢ ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶

Proof

Step	Hyp	Ref	Expression
1		prodeq1i.1	⊢ 𝐴 = 𝐵
2		prodeq1	⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 )
3	1 2	ax-mp	⊢ ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶