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Theorem xnegpnf 11417
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 11327 . 2  |-  -e +oo  =  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )
2 eqid 2443 . . 3  |- +oo  = +oo
32iftruei 3933 . 2  |-  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )  = -oo
41, 3eqtri 2472 1  |-  -e +oo  = -oo
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383   ifcif 3926   +oocpnf 9628   -oocmnf 9629   -ucneg 9811    -ecxne 11324
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-if 3927  df-xneg 11327
This theorem is referenced by:  xnegcl  11421  xnegneg  11422  xltnegi  11424  xnegid  11444  xnegdi  11449  xaddass2  11451  xsubge0  11462  xlesubadd  11464  xmulneg1  11470  xmulmnf1  11477  xadddi2  11498  xrsdsreclblem  18338  xblss2ps  20777  xblss2  20778  xaddeq0  27445
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