MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  negeqi Structured version   Unicode version

Theorem negeqi 9291
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 9290 . 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 1652   -ucneg 9284
This theorem is referenced by:  negsubdii  9377  recgt0ii  9908  m1expcl2  11395  crreczi  11496  absi  12083  geo2sum2  12643  sinhval  12747  coshval  12748  cos2bnd  12781  divalglem2  12907  ditg0  19732  cbvditg  19733  ang180lem2  20644  ang180lem3  20645  ang180lem4  20646  1cubrlem  20673  dcubic2  20676  atandm2  20709  efiasin  20720  asinsinlem  20723  asinsin  20724  asin1  20726  reasinsin  20728  atancj  20742  atantayl2  20770  ppiub  20980  lgseisenlem1  21125  lgseisenlem2  21126  lgsquadlem1  21130  ostth3  21324  nvpi  22147  ipidsq  22201  ipasslem10  22332  normlem1  22604  polid2i  22651  lnophmlem2  23512  xrge0iif1  24316  ballotlem2  24738  bpoly2  26095  bpoly3  26096  itg2addnclem3  26248  dvreasin  26280  areacirc  26288  m1expaddsub  27389  cnmsgnsubg  27402  lhe4.4ex1a  27514  itgsin0pilem1  27711  stoweidlem26  27742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-neg 9286
  Copyright terms: Public domain W3C validator