Theorem sumsn

Description: A sum of a singleton is the term. (Contributed by Mario Carneiro, 22-Apr-2014)

	Ref	Expression
Hypothesis	fsum1.1	⊢ ( 𝑘 = 𝑀 → 𝐴 = 𝐵 )
Assertion	sumsn	⊢ ( ( 𝑀 ∈ 𝑉 ∧ 𝐵 ∈ ℂ ) → Σ 𝑘 ∈ { 𝑀 } 𝐴 = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fsum1.1	⊢ ( 𝑘 = 𝑀 → 𝐴 = 𝐵 )
2		nfcv	⊢ Ⅎ 𝑘 𝐵
3	2 1	sumsnf	⊢ ( ( 𝑀 ∈ 𝑉 ∧ 𝐵 ∈ ℂ ) → Σ 𝑘 ∈ { 𝑀 } 𝐴 = 𝐵 )