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Theorem negeqi 9061
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 9060 . 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 1632   -ucneg 9054
This theorem is referenced by:  negsubdii  9147  recgt0ii  9678  m1expcl2  11141  crreczi  11242  absi  11787  geo2sum2  12346  sinhval  12450  coshval  12451  cos2bnd  12484  divalglem2  12610  ditg0  19219  cbvditg  19220  ang180lem2  20124  ang180lem3  20125  ang180lem4  20126  1cubrlem  20153  dcubic2  20156  atandm2  20189  efiasin  20200  asinsinlem  20203  asinsin  20204  asin1  20206  reasinsin  20208  atancj  20222  atantayl2  20250  ppiub  20459  lgseisenlem1  20604  lgseisenlem2  20605  lgsquadlem1  20609  ostth3  20803  nvpi  21248  ipidsq  21302  ipasslem10  21433  normlem1  21705  polid2i  21752  lnophmlem2  22613  ballotlem2  23063  xrge0iif1  23335  bpoly2  24864  bpoly3  24865  itg2addnc  25005  dvreasin  25026  areacirc  25034  m1expaddsub  27524  cnmsgnsubg  27537  lhe4.4ex1a  27649  itgsin0pilem1  27847  stoweidlem26  27878
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-neg 9056
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