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Metamath Proof Explorer

Theorem prodeq1iOLD

Description: Obsolete version of prodeq1i as of 1-Sep-2025. (Contributed by Scott Fenton, 4-Dec-2017) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	prodeq1iOLD.1	⊢ 𝐴 = 𝐵
	Assertion	prodeq1iOLD	⊢ ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶

Proof

Step	Hyp	Ref	Expression
1		prodeq1iOLD.1	⊢ 𝐴 = 𝐵
2		prodeq1	⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 )
3	1 2	ax-mp	⊢ ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶