Axiom ax-addrcl 7841

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7797. Proofs should normally use readdcl 7870 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 7743	. . . 4 class RR
3	1, 2	wcel 2135	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2135	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7747	. . . 4 class +
8	1, 4, 7	co 5836	. . 3 class ( A + B )
9	8, 2	wcel 2135	. 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  7870