MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-rnegex Unicode version

Axiom ax-rnegex 8808
Description: Existence of negative of real number. Axiom 15 of 22 for real and complex numbers, justified by theorem axrnegex 8784. (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 8736 . . 3  class  RR
31, 2wcel 1684 . 2  wff  A  e.  RR
4 vx . . . . . 6  set  x
54cv 1622 . . . . 5  class  x
6 caddc 8740 . . . . 5  class  +
71, 5, 6co 5858 . . . 4  class  ( A  +  x )
8 cc0 8737 . . . 4  class  0
97, 8wceq 1623 . . 3  wff  ( A  +  x )  =  0
109, 4, 2wrex 2544 . 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  8838  00id  8987  addid1  8992  cnegex  8993  renegcli  9108
  Copyright terms: Public domain W3C validator