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Axiom ax-rnegex 7741
Description: Existence of negative of real number. Axiom for real and complex numbers, justified by theorem axrnegex 7699. (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
StepHypRef Expression
1 cA . . 3  class  A
2 cr 7631 . . 3  class  RR
31, 2wcel 1480 . 2  wff  A  e.  RR
4 vx . . . . . 6  setvar  x
54cv 1330 . . . . 5  class  x
6 caddc 7635 . . . . 5  class  +
71, 5, 6co 5774 . . . 4  class  ( A  +  x )
8 cc0 7632 . . . 4  class  0
97, 8wceq 1331 . . 3  wff  ( A  +  x )  =  0
109, 4, 2wrex 2417 . 2  wff  E. x  e.  RR  ( A  +  x )  =  0
113, 10wi 4 1  wff  ( A  e.  RR  ->  E. x  e.  RR  ( A  +  x )  =  0 )
Colors of variables: wff set class
This axiom is referenced by:  0re  7778  readdcan  7914  cnegexlem1  7949  cnegexlem2  7950  cnegexlem3  7951  cnegex  7952  renegcl  8035  ltadd2  8193
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