Axiom ax-addrcl 7717

Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7673. Proofs should normally use readdcl 7746 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 7619	. . . 4 class RR
3	1, 2	wcel 1480	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		caddc 7623	. . . 4 class +
8	1, 4, 7	co 5774	. . 3 class ( A + B )
9	8, 2	wcel 1480	. 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  7746