Axiom ax-addrcl 8004

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7960. Proofs should normally use readdcl 8033 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 7906	. . . 4 class RR
3	1, 2	wcel 2175	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7910	. . . 4 class +
8	1, 4, 7	co 5934	. . 3 class ( A + B )
9	8, 2	wcel 2175	. 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  8033