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Metamath Proof Explorer

Theorem subcli

Description: Closure law for subtraction. (Contributed by NM, 26-Nov-1994) (Revised by Mario Carneiro, 21-Dec-2013)

Ref Expression
Hypotheses negidi.1 ⊢ A ∈ ℂ
pncan3i.2 ⊢ B ∈ ℂ
Assertion subcli ⊢ A − B ∈ ℂ

Proof

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