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Theorem negeqi 10594
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 10593 . 2 (𝐴 = 𝐵 → -𝐴 = -𝐵)
31, 2ax-mp 5 1 -𝐴 = -𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1658  -cneg 10586
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rex 3123  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4145  df-if 4307  df-sn 4398  df-pr 4400  df-op 4404  df-uni 4659  df-br 4874  df-iota 6086  df-fv 6131  df-ov 6908  df-neg 10588
This theorem is referenced by:  negsubdii  10687  recgt0ii  11259  m1expcl2  13176  crreczi  13283  absi  14403  geo2sum2  14979  bpoly2  15160  bpoly3  15161  sinhval  15256  coshval  15257  cos2bnd  15290  divalglem2  15492  m1expaddsub  18269  cnmsgnsubg  20282  psgninv  20287  ncvspi  23325  cphipval2  23409  ditg0  24016  cbvditg  24017  ang180lem2  24950  ang180lem3  24951  ang180lem4  24952  1cubrlem  24981  dcubic2  24984  atandm2  25017  efiasin  25028  asinsinlem  25031  asinsin  25032  asin1  25034  reasinsin  25036  atancj  25050  atantayl2  25078  ppiub  25342  lgseisenlem1  25513  lgseisenlem2  25514  lgsquadlem1  25518  ostth3  25740  nvpi  28077  ipidsq  28120  ipasslem10  28249  normlem1  28522  polid2i  28569  lnophmlem2  29431  archirngz  30288  xrge0iif1  30529  ballotlem2  31096  itg2addnclem3  34006  dvasin  34039  areacirc  34048  lhe4.4ex1a  39368  itgsin0pilem1  40960  stoweidlem26  41037  dirkertrigeqlem3  41111  fourierdlem103  41220  sqwvfourb  41240  fourierswlem  41241  proththd  42361
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