Axiom ax-addrcl 7829

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7785. Proofs should normally use readdcl 7858 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

Step	Hyp	Ref	Expression
1		cA	. . . 4 class 𝐴
2		cr 7731	. . . 4 class ℝ
3	1, 2	wcel 2128	. . 3 wff 𝐴 ∈ ℝ
4		cB	. . . 4 class 𝐵
5	4, 2	wcel 2128	. . 3 wff 𝐵 ∈ ℝ
6	3, 5	wa 103	. 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7		caddc 7735	. . . 4 class +
8	1, 4, 7	co 5824	. . 3 class (𝐴 + 𝐵)
9	8, 2	wcel 2128	. 2 wff (𝐴 + 𝐵) ∈ ℝ
10	6, 9	wi 4	1 wff ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)

This axiom is referenced by:  readdcl  7858