Axiom ax-addrcl 8269

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8225. Proofs should normally use readdcl 8298 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 8171	. . . 4 class RR
3	1, 2	wcel 2209	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2209	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 8175	. . . 4 class +
8	1, 4, 7	co 6078	. . 3 class ( A + B )
9	8, 2	wcel 2209	. 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  8298