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Metamath Proof Explorer

Theorem prodeq2sdvOLD

Description: Obsolete version of prodeq2sdv as of 1-Sep-2025. (Contributed by Scott Fenton, 4-Dec-2017) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	prodeq2sdvOLD.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
	Assertion	prodeq2sdvOLD	⊢ ( 𝜑 → ∏ 𝑘 ∈ 𝐴 𝐵 = ∏ 𝑘 ∈ 𝐴 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		prodeq2sdvOLD.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝑘 ∈ 𝐴 ) → 𝐵 = 𝐶 )
3	2	prodeq2dv	⊢ ( 𝜑 → ∏ 𝑘 ∈ 𝐴 𝐵 = ∏ 𝑘 ∈ 𝐴 𝐶 )