Axiom ax-addrcl 8189

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8145. Proofs should normally use readdcl 8218 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 8091	. . . 4 class ℝ
3	1, 2	wcel 2202	. . 3 wff 𝐴 ∈ ℝ
4		cB	. . . 4 class 𝐵
5	4, 2	wcel 2202	. . 3 wff 𝐵 ∈ ℝ
6	3, 5	wa 104	. 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7		caddc 8095	. . . 4 class +
8	1, 4, 7	co 6028	. . 3 class (𝐴 + 𝐵)
9	8, 2	wcel 2202	. 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  8218