Axiom ax-addrcl 6981

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6941. Proofs should normally use readdcl 7007 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 6888	. . . 4 class ℝ
3	1, 2	wcel 1393	. . 3 wff 𝐴 ∈ ℝ
4		cB	. . . 4 class 𝐵
5	4, 2	wcel 1393	. . 3 wff 𝐵 ∈ ℝ
6	3, 5	wa 97	. 2 wff (𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ)
7		caddc 6892	. . . 4 class +
8	1, 4, 7	co 5512	. . 3 class (𝐴 + 𝐵)
9	8, 2	wcel 1393	. 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  7007