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Metamath Proof Explorer

Theorem sumeq2i

Description: Equality inference for sum. (Contributed by NM, 3-Dec-2005)

Ref Expression
Hypothesis sumeq2i.1 ⊢ k ∈ A → B = C
Assertion sumeq2i ⊢ ∑ k ∈ A B = ∑ k ∈ A C

Proof

Step Hyp Ref Expression
1 sumeq2i.1 ⊢ k ∈ A → B = C
2 sumeq2 ⊢ ∀ k ∈ A B = C → ∑ k ∈ A B = ∑ k ∈ A C
3 2 1 mprg ⊢ ∑ k ∈ A B = ∑ k ∈ A C