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CHAPTER II [:] The Real Number System [...] 1. THE FIELD PROPERTIES. "end quote
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F6:       -(-a) = a

For any real number   a,    -(-a) = a
  0  
  =  
  -(-a) + (-a)  
  existence of additive inverse  
  But  
   
   
  we also have  
  0  
  =  
  a + (-a)  
  existence of additive inverse  
  And  
   
   
  both of the above equations are of the form  
  0  
  =  
  x + (-a)  
  And therefore we have the desired result by F3.  

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