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Theorem xnegpnf 11291
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 11201 . 2  |-  -e +oo  =  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )
2 eqid 2454 . . 3  |- +oo  = +oo
32iftruei 3907 . 2  |-  if ( +oo  = +oo , -oo ,  if ( +oo  = -oo , +oo ,  -u +oo ) )  = -oo
41, 3eqtri 2483 1  |-  -e +oo  = -oo
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   ifcif 3900   +oocpnf 9527   -oocmnf 9528   -ucneg 9708    -ecxne 11198
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-if 3901  df-xneg 11201
This theorem is referenced by:  xnegcl  11295  xnegneg  11296  xltnegi  11298  xnegid  11318  xnegdi  11323  xaddass2  11325  xsubge0  11336  xlesubadd  11338  xmulneg1  11344  xmulmnf1  11351  xadddi2  11372  xrsdsreclblem  17985  xblss2ps  20109  xblss2  20110  xaddeq0  26198
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