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Axiom ax-rnegex 8804
Description: Existence of negative of real number. Axiom 15 of 22 for real and complex numbers, justified by theorem axrnegex 8780. (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 8732 . . 3  class  RR
31, 2wcel 1685 . 2  wff  A  e.  RR
4 vx . . . . . 6  set  x
54cv 1623 . . . . 5  class  x
6 caddc 8736 . . . . 5  class  +
71, 5, 6co 5820 . . . 4  class  ( A  +  x )
8 cc0 8733 . . . 4  class  0
97, 8wceq 1624 . . 3  wff  ( A  +  x )  =  0
109, 4, 2wrex 2546 . 2  wff  E. x  e.  RR  ( A  +  x )  =  0
113, 10wi 6 1  wff  ( A  e.  RR  ->  E. x  e.  RR  ( A  +  x )  =  0 )
Colors of variables: wff set class
This axiom is referenced by:  0re  8834  00id  8983  addid1  8988  cnegex  8989  renegcli  9104
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