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Theorem negeqi 9595
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 9594 . 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 1369   -ucneg 9588
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2716  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-sn 3873  df-pr 3875  df-op 3879  df-uni 4087  df-br 4288  df-iota 5376  df-fv 5421  df-ov 6089  df-neg 9590
This theorem is referenced by:  negsubdii  9685  recgt0ii  10230  m1expcl2  11879  crreczi  11981  absi  12767  geo2sum2  13326  sinhval  13430  coshval  13431  cos2bnd  13464  divalglem2  13591  m1expaddsub  15995  cnmsgnsubg  17982  psgninv  17987  ditg0  21303  cbvditg  21304  ang180lem2  22181  ang180lem3  22182  ang180lem4  22183  1cubrlem  22211  dcubic2  22214  atandm2  22247  efiasin  22258  asinsinlem  22261  asinsin  22262  asin1  22264  reasinsin  22266  atancj  22280  atantayl2  22308  ppiub  22518  lgseisenlem1  22663  lgseisenlem2  22664  lgsquadlem1  22668  ostth3  22862  nvpi  24005  ipidsq  24059  ipasslem10  24190  normlem1  24463  polid2i  24510  lnophmlem2  25372  archirngz  26157  xrge0iif1  26320  ballotlem2  26823  bpoly2  28151  bpoly3  28152  itg2addnclem3  28398  dvasin  28433  areacirc  28442  lhe4.4ex1a  29556  itgsin0pilem1  29743  stoweidlem26  29774
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