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Metamath Proof Explorer

Theorem subnegi

Description: Relationship between subtraction and negative. (Contributed by NM, 1-Dec-2005)

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

Proof

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