Theorem sumeq1i

Description: Equality inference for sum. (Contributed by NM, 2-Jan-2006)

	Ref	Expression
Hypothesis	sumeq1i.1	⊢ 𝐴 = 𝐵
Assertion	sumeq1i	⊢ Σ 𝑘 ∈ 𝐴 𝐶 = Σ 𝑘 ∈ 𝐵 𝐶

Proof

Step	Hyp	Ref	Expression
1		sumeq1i.1	⊢ 𝐴 = 𝐵
2		sumeq1	⊢ ( 𝐴 = 𝐵 → Σ 𝑘 ∈ 𝐴 𝐶 = Σ 𝑘 ∈ 𝐵 𝐶 )
3	1 2	ax-mp	⊢ Σ 𝑘 ∈ 𝐴 𝐶 = Σ 𝑘 ∈ 𝐵 𝐶