Theorem prodeq2i

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

	Ref	Expression
Hypothesis	prodeq2i.1	⊢ ( 𝑘 ∈ 𝐴 → 𝐵 = 𝐶 )
Assertion	prodeq2i	⊢ ∏ 𝑘 ∈ 𝐴 𝐵 = ∏ 𝑘 ∈ 𝐴 𝐶

Proof

Step	Hyp	Ref	Expression
1		prodeq2i.1	⊢ ( 𝑘 ∈ 𝐴 → 𝐵 = 𝐶 )
2		prodeq2	⊢ ( ∀ 𝑘 ∈ 𝐴 𝐵 = 𝐶 → ∏ 𝑘 ∈ 𝐴 𝐵 = ∏ 𝑘 ∈ 𝐴 𝐶 )
3	2 1	mprg	⊢ ∏ 𝑘 ∈ 𝐴 𝐵 = ∏ 𝑘 ∈ 𝐴 𝐶