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Axiom ax-addrcl 9853
Description: Closure law for addition in the real subfield of complex numbers. Axiom 6 of 23 for real and complex numbers, justified by theorem axaddrcl 9829. Proofs should normally use readdcl 9875 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 9791 . . . 4 class
31, 2wcel 1976 . . 3 wff 𝐴 ∈ ℝ
4 cB . . . 4 class 𝐵
54, 2wcel 1976 . . 3 wff 𝐵 ∈ ℝ
63, 5wa 382 . 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7 caddc 9795 . . . 4 class +
81, 4, 7co 6526 . . 3 class (𝐴 + 𝐵)
98, 2wcel 1976 . 2 wff (𝐴 + 𝐵) ∈ ℝ
106, 9wi 4 1 wff ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)
Colors of variables: wff setvar class
This axiom is referenced by:  readdcl  9875
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