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Theorem negeqi 9867
Description: Equality inference for negatives. (Contributed by NM, 14-Feb-1995.)
Hypothesis
Ref Expression
negeqi.1  |-  A  =  B
Assertion
Ref Expression
negeqi  |-  -u A  =  -u B

Proof of Theorem negeqi
StepHypRef Expression
1 negeqi.1 . 2  |-  A  =  B
2 negeq 9866 . 2  |-  ( A  =  B  ->  -u A  =  -u B )
31, 2ax-mp 5 1  |-  -u A  =  -u B
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   -ucneg 9860
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-iota 5565  df-fv 5609  df-ov 6308  df-neg 9862
This theorem is referenced by:  negsubdii  9959  recgt0ii  10512  m1expcl2  12291  crreczi  12394  absi  13328  geo2sum2  13908  bpoly2  14088  bpoly3  14089  sinhval  14186  coshval  14187  cos2bnd  14220  divalglem2  14351  m1expaddsub  17090  cnmsgnsubg  19076  psgninv  19081  ditg0  22685  cbvditg  22686  ang180lem2  23604  ang180lem3  23605  ang180lem4  23606  1cubrlem  23632  dcubic2  23635  atandm2  23668  efiasin  23679  asinsinlem  23682  asinsin  23683  asin1  23685  reasinsin  23687  atancj  23701  atantayl2  23729  ppiub  23995  lgseisenlem1  24140  lgseisenlem2  24141  lgsquadlem1  24145  ostth3  24339  nvpi  26140  ipidsq  26194  ipasslem10  26325  normlem1  26598  polid2i  26645  lnophmlem2  27505  archirngz  28344  xrge0iif1  28583  ballotlem2  29147  itg2addnclem3  31698  dvasin  31731  areacirc  31740  lhe4.4ex1a  36314  itgsin0pilem1  37394  stoweidlem26  37454  dirkertrigeqlem3  37530  fourierdlem103  37640  sqwvfourb  37660  fourierswlem  37661  proththd  38303
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