Axiom ax-addrcl 7073

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7033. Proofs should normally use readdcl 7099 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 6980	. . . 4 class RR
3	1, 2	wcel 1433	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1433	. . 3 wff B e. RR
6	3, 5	wa 102	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 6984	. . . 4 class +
8	1, 4, 7	co 5532	. . 3 class ( A + B )
9	8, 2	wcel 1433	. 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  7099