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Axiom ax-addcl 7591
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7551. Proofs should normally use addcl 7617 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 7498 . . . 4 class
31, 2wcel 1448 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1448 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 103 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 caddc 7503 . . . 4 class +
81, 4, 7co 5706 . . 3 class (𝐴 + 𝐵)
98, 2wcel 1448 . 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  7617
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