Axiom ax-addrcl 11179

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 11155. Proofs should normally use readdcl 11201 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 11117	. . . 4 class ℝ
3	1, 2	wcel 2146	. . 3 wff 𝐴 ∈ ℝ
4		cB	. . . 4 class 𝐵
5	4, 2	wcel 2146	. . 3 wff 𝐵 ∈ ℝ
6	3, 5	wa 401	. 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7		caddc 11121	. . . 4 class +
8	1, 4, 7	co 7423	. . 3 class (𝐴 + 𝐵)
9	8, 2	wcel 2146	. 2 wff (𝐴 + 𝐵) ∈ ℝ
10	6, 9	wi 4	1 wff ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ)

This axiom is used by:  readdcl  11201