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Theorem negeqi 9304
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 9303 . 2  |-  ( A  =  B  ->  -u A  =  -u B )
31, 2ax-mp 5 1  |-  -u A  =  -u B
Colors of variables: wff set class
Syntax hints:    = wceq 1653   -ucneg 9297
This theorem is referenced by:  negsubdii  9390  recgt0ii  9921  m1expcl2  11408  crreczi  11509  absi  12096  geo2sum2  12656  sinhval  12760  coshval  12761  cos2bnd  12794  divalglem2  12920  ditg0  19745  cbvditg  19746  ang180lem2  20657  ang180lem3  20658  ang180lem4  20659  1cubrlem  20686  dcubic2  20689  atandm2  20722  efiasin  20733  asinsinlem  20736  asinsin  20737  asin1  20739  reasinsin  20741  atancj  20755  atantayl2  20783  ppiub  20993  lgseisenlem1  21138  lgseisenlem2  21139  lgsquadlem1  21143  ostth3  21337  nvpi  22160  ipidsq  22214  ipasslem10  22345  normlem1  22617  polid2i  22664  lnophmlem2  23525  xrge0iif1  24329  ballotlem2  24751  bpoly2  26108  bpoly3  26109  itg2addnclem3  26272  dvreasin  26304  areacirc  26311  m1expaddsub  27412  cnmsgnsubg  27425  lhe4.4ex1a  27537  itgsin0pilem1  27734  stoweidlem26  27765
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087  df-neg 9299
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