Theorem sumeq2sdvOLD

Description: Obsolete version of sumeq2sdv as of 14-Aug-2025. (Contributed by NM, 3-Jan-2006) (Proof shortened by Glauco Siliprandi, 5-Apr-2020) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sumeq2sdvOLD.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	sumeq2sdvOLD	⊢ ( 𝜑 → Σ 𝑘 ∈ 𝐴 𝐵 = Σ 𝑘 ∈ 𝐴 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		sumeq2sdvOLD.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
2	1	ralrimivw	⊢ ( 𝜑 → ∀ 𝑘 ∈ 𝐴 𝐵 = 𝐶 )
3	2	sumeq2d	⊢ ( 𝜑 → Σ 𝑘 ∈ 𝐴 𝐵 = Σ 𝑘 ∈ 𝐴 𝐶 )