Axiom ax-addrcl 8276

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8232. Proofs should normally use readdcl 8305 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 8178	. . . 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 8182	. . . 4 class +
8	1, 4, 7	co 6085	. . 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 used by:  readdcl  8305