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Theorem negeqi 10476
Description: Equality inference for negatives. (Contributed by NM, 14-Feb-1995.)
Hypothesis
Ref Expression
negeqi.1 𝐴 = 𝐵
Assertion
Ref Expression
negeqi -𝐴 = -𝐵

Proof of Theorem negeqi
StepHypRef Expression
1 negeqi.1 . 2 𝐴 = 𝐵
2 negeq 10475 . 2 (𝐴 = 𝐵 → -𝐴 = -𝐵)
31, 2ax-mp 5 1 -𝐴 = -𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  -cneg 10469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rex 3067  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-uni 4575  df-br 4787  df-iota 5994  df-fv 6039  df-ov 6796  df-neg 10471
This theorem is referenced by:  negsubdii  10568  recgt0ii  11131  m1expcl2  13089  crreczi  13196  absi  14234  geo2sum2  14812  bpoly2  14994  bpoly3  14995  sinhval  15090  coshval  15091  cos2bnd  15124  divalglem2  15326  m1expaddsub  18125  cnmsgnsubg  20138  psgninv  20143  ncvspi  23175  cphipval2  23259  ditg0  23837  cbvditg  23838  ang180lem2  24761  ang180lem3  24762  ang180lem4  24763  1cubrlem  24789  dcubic2  24792  atandm2  24825  efiasin  24836  asinsinlem  24839  asinsin  24840  asin1  24842  reasinsin  24844  atancj  24858  atantayl2  24886  ppiub  25150  lgseisenlem1  25321  lgseisenlem2  25322  lgsquadlem1  25326  ostth3  25548  nvpi  27862  ipidsq  27905  ipasslem10  28034  normlem1  28307  polid2i  28354  lnophmlem2  29216  archirngz  30083  xrge0iif1  30324  ballotlem2  30890  itg2addnclem3  33795  dvasin  33828  areacirc  33837  lhe4.4ex1a  39054  itgsin0pilem1  40683  stoweidlem26  40760  dirkertrigeqlem3  40834  fourierdlem103  40943  sqwvfourb  40963  fourierswlem  40964  proththd  42059
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