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Axiom ax-addcl 7937
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 7893. Proofs should normally use addcl 7966 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) ∈ ℂ)

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4 class 𝐴
2 cc 7839 . . . 4 class
31, 2wcel 2160 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 2160 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 104 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 caddc 7844 . . . 4 class +
81, 4, 7co 5896 . . 3 class (𝐴 + 𝐵)
98, 2wcel 2160 . 2 wff (𝐴 + 𝐵) ∈ ℂ
106, 9wi 4 1 wff ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) ∈ ℂ)
Colors of variables: wff set class
This axiom is referenced by:  addcl  7966
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