Axiom ax-addrcl 7850

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7806. Proofs should normally use readdcl 7879 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 7752	. . . 4 class RR
3	1, 2	wcel 2136	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2136	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7756	. . . 4 class +
8	1, 4, 7	co 5842	. . 3 class ( A + B )
9	8, 2	wcel 2136	. 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  7879