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Theorem xnegpnf 10741
 Description: Minus . Remark of [BourbakiTop1] p. IV.15. (Contributed by FL, 26-Dec-2011.)
Assertion
Ref Expression
xnegpnf

Proof of Theorem xnegpnf
StepHypRef Expression
1 df-xneg 10656 . 2
2 eqid 2401 . . 3
3 iftrue 3702 . . 3
42, 3ax-mp 8 . 2
51, 4eqtri 2421 1
 Colors of variables: wff set class Syntax hints:   wceq 1649  cif 3696   cpnf 9064   cmnf 9065  cneg 9238   cxne 10653 This theorem is referenced by:  xnegcl  10745  xnegneg  10746  xltnegi  10748  xnegid  10768  xnegdi  10773  xaddass2  10775  xsubge0  10786  xlesubadd  10788  xmulneg1  10794  xmulmnf1  10801  xadddi2  10822  xrsdsreclblem  16681  xblss2  18346  xaddeq0  24044 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-if 3697  df-xneg 10656
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