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Axiom ax-addrcl 7907
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7863. Proofs should normally use readdcl 7936 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 7809 . . . 4 class
31, 2wcel 2148 . . 3 wff 𝐴 ∈ ℝ
4 cB . . . 4 class 𝐵
54, 2wcel 2148 . . 3 wff 𝐵 ∈ ℝ
63, 5wa 104 . 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7 caddc 7813 . . . 4 class +
81, 4, 7co 5874 . . 3 class (𝐴 + 𝐵)
98, 2wcel 2148 . 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  7936
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