Axiom ax-addrcl 8129

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8085. Proofs should normally use readdcl 8158 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 8031	. . . 4 class RR
3	1, 2	wcel 2202	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2202	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 8035	. . . 4 class +
8	1, 4, 7	co 6018	. . 3 class ( A + B )
9	8, 2	wcel 2202	. 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  8158