Axiom ax-rnegex 8129

Description: Existence of negative of real number. Axiom for real and complex numbers, justified by Theorem axrnegex 8087. (Contributed by Eric Schmidt, 21-May-2007.)

Assertion

Ref	Expression
ax-rnegex	|- ( A e. RR -> E. x e. RR ( A + x ) = 0 )

Distinct variable group:   x, A

Detailed syntax breakdown of Axiom ax-rnegex

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cr 8019	. . 3 class RR
3	1, 2	wcel 2200	. 2 wff A e. RR
4		vx	. . . . . 6 setvar x
5	4	cv 1394	. . . . 5 class x
6		caddc 8023	. . . . 5 class +
7	1, 5, 6	co 6011	. . . 4 class ( A + x )
8		cc0 8020	. . . 4 class 0
9	7, 8	wceq 1395	. . 3 wff ( A + x ) = 0
10	9, 4, 2	wrex 2509	. 2 wff E. x e. RR ( A + x ) = 0
11	3, 10	wi 4	1 wff ( A e. RR -> E. x e. RR ( A + x ) = 0 )

This axiom is referenced by:  0re  8167  readdcan  8307  cnegexlem1  8342  cnegexlem2  8343  cnegexlem3  8344  cnegex  8345  renegcl  8428  ltadd2  8587