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Definition df-xneg 10448
Description: Define the negative of an extended real number. (Contributed by FL, 26-Dec-2011.)
Assertion
Ref Expression
df-xneg  |-  - e A  =  if ( A  =  +oo ,  -oo ,  if ( A  = 
-oo ,  +oo ,  -u A ) )

Detailed syntax breakdown of Definition df-xneg
StepHypRef Expression
1 cA . . 3  class  A
21cxne 10445 . 2  class  - e A
3 cpnf 8860 . . . 4  class  +oo
41, 3wceq 1624 . . 3  wff  A  = 
+oo
5 cmnf 8861 . . 3  class  -oo
61, 5wceq 1624 . . . 4  wff  A  = 
-oo
71cneg 9034 . . . 4  class  -u A
86, 3, 7cif 3567 . . 3  class  if ( A  =  -oo ,  +oo ,  -u A )
94, 5, 8cif 3567 . 2  class  if ( A  =  +oo ,  -oo ,  if ( A  =  -oo ,  +oo , 
-u A ) )
102, 9wceq 1624 1  wff  - e A  =  if ( A  =  +oo ,  -oo ,  if ( A  = 
-oo ,  +oo ,  -u A ) )
Colors of variables: wff set class
This definition is referenced by:  xnegeq  10529  xnegex  10530  xnegpnf  10531  xnegmnf  10532  rexneg  10533
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