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Theorem negeqd 7624
Description: Equality deduction for negatives. (Contributed by NM, 14-May-1999.)
Hypothesis
Ref Expression
negeqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
negeqd  |-  ( ph  -> 
-u A  =  -u B )

Proof of Theorem negeqd
StepHypRef Expression
1 negeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 negeq 7622 . 2  |-  ( A  =  B  ->  -u A  =  -u B )
31, 2syl 14 1  |-  ( ph  -> 
-u A  =  -u B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   -ucneg 7601
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3639  df-br 3823  df-iota 4948  df-fv 4991  df-ov 5618  df-neg 7603
This theorem is referenced by:  negdi  7686  mulneg2  7821  mulm1  7825  mulreim  8025  apneg  8032  divnegap  8115  div2negap  8144  recgt0  8249  infrenegsupex  9017  supminfex  9020  ceilqval  9644  ceilid  9653  modqcyc2  9698  monoord2  9830  reneg  10219  imneg  10227  cjcj  10234  cjneg  10241  minmax  10577  odd2np1  10798  oexpneg  10802  modgcd  10907  ex-ceil  11142
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