Theorem cbvesumv

Description: Change bound variable in an extended sum. (Contributed by Thierry Arnoux, 19-Jun-2017)

	Ref	Expression
Hypothesis	cbvesum.1	⊢ ( 𝑗 = 𝑘 → 𝐵 = 𝐶 )
Assertion	cbvesumv	⊢ Σ* 𝑗 ∈ 𝐴 𝐵 = Σ* 𝑘 ∈ 𝐴 𝐶

Proof

Step	Hyp	Ref	Expression
1		cbvesum.1	⊢ ( 𝑗 = 𝑘 → 𝐵 = 𝐶 )
2		nfcv	⊢ Ⅎ 𝑘 𝐴
3		nfcv	⊢ Ⅎ 𝑗 𝐴
4		nfcv	⊢ Ⅎ 𝑘 𝐵
5		nfcv	⊢ Ⅎ 𝑗 𝐶
6	1 2 3 4 5	cbvesum	⊢ Σ* 𝑗 ∈ 𝐴 𝐵 = Σ* 𝑘 ∈ 𝐴 𝐶