Axiom ax-addrcl 8226

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8182. Proofs should normally use readdcl 8255 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-addrcl	|- ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )

Detailed syntax breakdown of Axiom ax-addrcl

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cr 8128	. . . 4 class RR
3	1, 2	wcel 2205	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2205	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 8132	. . . 4 class +
8	1, 4, 7	co 6052	. . 3 class ( A + B )
9	8, 2	wcel 2205	. 2 wff ( A + B ) e. RR
10	6, 9	wi 4	1 wff ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )

This axiom is referenced by:  readdcl  8255