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Theorem negeqi 9045
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 9044 . 2  |-  ( A  =  B  ->  -u A  =  -u B )
31, 2ax-mp 8 1  |-  -u A  =  -u B
Colors of variables: wff set class
Syntax hints:    = wceq 1623   -ucneg 9038
This theorem is referenced by:  negsubdii  9131  recgt0ii  9662  m1expcl2  11125  crreczi  11226  absi  11771  geo2sum2  12330  sinhval  12434  coshval  12435  cos2bnd  12468  divalglem2  12594  ditg0  19203  cbvditg  19204  ang180lem2  20108  ang180lem3  20109  ang180lem4  20110  1cubrlem  20137  dcubic2  20140  atandm2  20173  efiasin  20184  asinsinlem  20187  asinsin  20188  asin1  20190  reasinsin  20192  atancj  20206  atantayl2  20234  ppiub  20443  lgseisenlem1  20588  lgseisenlem2  20589  lgsquadlem1  20593  ostth3  20787  nvpi  21232  ipidsq  21286  ipasslem10  21417  normlem1  21689  polid2i  21736  lnophmlem2  22597  ballotlem2  23047  xrge0iif1  23320  bpoly2  24792  bpoly3  24793  dvreasin  24923  areacirc  24931  m1expaddsub  27421  cnmsgnsubg  27434  lhe4.4ex1a  27546  itgsin0pilem1  27744  stoweidlem26  27775
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-neg 9040
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