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Theorem negeq 7204
Description: Equality theorem for negatives. (Contributed by NM, 10-Feb-1995.)
Assertion
Ref Expression
negeq  |-  ( A  =  B  ->  -u A  =  -u B )

Proof of Theorem negeq
StepHypRef Expression
1 oveq2 5520 . 2  |-  ( A  =  B  ->  (
0  -  A )  =  ( 0  -  B ) )
2 df-neg 7185 . 2  |-  -u A  =  ( 0  -  A )
3 df-neg 7185 . 2  |-  -u B  =  ( 0  -  B )
41, 2, 33eqtr4g 2097 1  |-  ( A  =  B  ->  -u A  =  -u B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1243  (class class class)co 5512   0cc0 6889    - cmin 7182   -ucneg 7183
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-neg 7185
This theorem is referenced by:  negeqi  7205  negeqd  7206  neg11  7262  recexre  7569  elz  8247  znegcl  8276  zaddcllemneg  8284  elz2  8312  zindd  8356  ublbneg  8548  eqreznegel  8549  negm  8550  qnegcl  8571  xnegeq  8740  ceilqval  9148  expival  9257  expnegap0  9263  m1expcl2  9277  ex-ceil  9896
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