Axiom ax-addrcl 8107

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 8063. Proofs should normally use readdcl 8136 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 8009	. . . 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 8013	. . . 4 class +
8	1, 4, 7	co 6007	. . 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  8136