Axiom ax-addrcl 6760

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6731. Proofs should normally use readdcl 6785 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 6690	. . . 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 6694	. . . 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  6785