Axiom ax-addrcl

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 . Proofs should normally use readdcl instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994)

	Ref	Expression
Assertion	ax-addrcl	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ) → ( 𝐴 + 𝐵 ) ∈ ℝ )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	⊢ 𝐴
1		cr	⊢ ℝ
2	0 1	wcel	⊢ 𝐴 ∈ ℝ
3		cB	⊢ 𝐵
4	3 1	wcel	⊢ 𝐵 ∈ ℝ
5	2 4	wa	⊢ ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ )
6		caddc	⊢ +
7	0 3 6	co	⊢ ( 𝐴 + 𝐵 )
8	7 1	wcel	⊢ ( 𝐴 + 𝐵 ) ∈ ℝ
9	5 8	wi	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ) → ( 𝐴 + 𝐵 ) ∈ ℝ )