Axiom ax-addrcl 8057

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8013. Proofs should normally use readdcl 8086 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 7959	. . . 4 class RR
3	1, 2	wcel 2178	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2178	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7963	. . . 4 class +
8	1, 4, 7	co 5967	. . 3 class ( A + B )
9	8, 2	wcel 2178	. 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  8086