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Axiom ax-addcl 6980
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 6940. Proofs should normally use addcl 7006 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 6887 . . . 4 class
31, 2wcel 1393 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1393 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 97 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 caddc 6892 . . . 4 class +
81, 4, 7co 5512 . . 3 class (𝐴 + 𝐵)
98, 2wcel 1393 . 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  7006
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