Axiom ax-addrcl 8042

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddrcl 7998. Proofs should normally use readdcl 8071 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 7944	. . . 4 class RR
3	1, 2	wcel 2177	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2177	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7948	. . . 4 class +
8	1, 4, 7	co 5957	. . 3 class ( A + B )
9	8, 2	wcel 2177	. 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  8071