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Metamath Proof Explorer

Theorem addcli

Description: Closure law for addition. (Contributed by NM, 23-Nov-1994)

Ref Expression
Hypotheses axi.1 ⊢ A ∈ ℂ
axi.2 ⊢ B ∈ ℂ
Assertion addcli ⊢ A + B ∈ ℂ

Proof

Step Hyp Ref Expression
1 axi.1 ⊢ A ∈ ℂ
2 axi.2 ⊢ B ∈ ℂ
3 addcl ⊢ A ∈ ℂ ∧ B ∈ ℂ → A + B ∈ ℂ
4 1 2 3 mp2an ⊢ A + B ∈ ℂ