Axiom ax-addrcl 8092

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8048. Proofs should normally use readdcl 8121 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 7994	. . . 4 class RR
3	1, 2	wcel 2200	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2200	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7998	. . . 4 class +
8	1, 4, 7	co 6000	. . 3 class ( A + B )
9	8, 2	wcel 2200	. 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  8121