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Definition df-xneg 9499
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 9496 . 2  class  -e
A
3 cpnf 7761 . . . 4  class +oo
41, 3wceq 1314 . . 3  wff  A  = +oo
5 cmnf 7762 . . 3  class -oo
61, 5wceq 1314 . . . 4  wff  A  = -oo
71cneg 7898 . . . 4  class  -u A
86, 3, 7cif 3442 . . 3  class  if ( A  = -oo , +oo ,  -u A )
94, 5, 8cif 3442 . 2  class  if ( A  = +oo , -oo ,  if ( A  = -oo , +oo ,  -u A ) )
102, 9wceq 1314 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  9550  xnegpnf  9551  xnegmnf  9552  rexneg  9553
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