Axiom ax-addrcl 6780

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6751. Proofs should normally use readdcl 6805 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 6710	. . . 4 class ℝ
3	1, 2	wcel 1390	. . 3 wff A ∈ ℝ
4		cB	. . . 4 class B
5	4, 2	wcel 1390	. . 3 wff B ∈ ℝ
6	3, 5	wa 97	. 2 wff (A ∈ ℝ ∧ B ∈ ℝ)
7		caddc 6714	. . . 4 class +
8	1, 4, 7	co 5455	. . 3 class (A + B)
9	8, 2	wcel 1390	. 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  6805