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Axiom ax-addrcl 6979
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6939. Proofs should normally use readdcl 7005 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addrcl ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)

Detailed syntax breakdown of Axiom ax-addrcl
StepHypRef Expression
1 cA . . . 4 class 𝐴
2 cr 6886 . . . 4 class
31, 2wcel 1393 . . 3 wff 𝐴 ∈ ℝ
4 cB . . . 4 class 𝐵
54, 2wcel 1393 . . 3 wff 𝐵 ∈ ℝ
63, 5wa 97 . 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7 caddc 6890 . . . 4 class +
81, 4, 7co 5512 . . 3 class (𝐴 + 𝐵)
98, 2wcel 1393 . 2 wff (𝐴 + 𝐵) ∈ ℝ
106, 9wi 4 1 wff ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)
Colors of variables: wff set class
This axiom is referenced by:  readdcl  7005
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