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Axiom ax-addrcl 7039
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6999. Proofs should normally use readdcl 7065 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 6946 . . . 4 class
31, 2wcel 1409 . . 3 wff 𝐴 ∈ ℝ
4 cB . . . 4 class 𝐵
54, 2wcel 1409 . . 3 wff 𝐵 ∈ ℝ
63, 5wa 101 . 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7 caddc 6950 . . . 4 class +
81, 4, 7co 5540 . . 3 class (𝐴 + 𝐵)
98, 2wcel 1409 . 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  7065
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