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Theorem xnegpnf 9604
Description: Minus +oo. Remark of [BourbakiTop1] p. IV.15. (Contributed by FL, 26-Dec-2011.)
Assertion
Ref Expression
xnegpnf  |-  -e +oo  = -oo

Proof of Theorem xnegpnf
StepHypRef Expression
1 df-xneg 9552 . 2  |-  -e +oo  =  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )
2 eqid 2137 . . 3  |- +oo  = +oo
32iftruei 3475 . 2  |-  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )  = -oo
41, 3eqtri 2158 1  |-  -e +oo  = -oo
Colors of variables: wff set class
Syntax hints:    = wceq 1331   ifcif 3469   +oocpnf 7790   -oocmnf 7791   -ucneg 7927    -ecxne 9549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-if 3470  df-xneg 9552
This theorem is referenced by:  xnegcl  9608  xnegneg  9609  xltnegi  9611  xnegid  9635  xnegdi  9644  xaddass2  9646  xsubge0  9657  xposdif  9658  xlesubadd  9659  xblss2ps  12562  xblss2  12563
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