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Metamath Proof Explorer

Theorem negdii

Description: Distribution of negative over addition. (Contributed by NM, 28-Jul-1999) (Proof shortened by OpenAI, 25-Mar-2011)

Ref Expression
Hypotheses negidi.1 ⊢ A ∈ ℂ
pncan3i.2 ⊢ B ∈ ℂ
Assertion negdii ⊢ − A + B = - A + − B

Proof

Step Hyp Ref Expression
1 negidi.1 ⊢ A ∈ ℂ
2 pncan3i.2 ⊢ B ∈ ℂ
3 negdi ⊢ A ∈ ℂ ∧ B ∈ ℂ → − A + B = - A + − B
4 1 2 3 mp2an ⊢ − A + B = - A + − B