Axiom ax-addrcl 7592

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7552. Proofs should normally use readdcl 7618 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 7499	. . . 4 class RR
3	1, 2	wcel 1448	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1448	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7503	. . . 4 class +
8	1, 4, 7	co 5706	. . 3 class ( A + B )
9	8, 2	wcel 1448	. 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  7618