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Theorem negeqd 7774
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 7772 . 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 1296   -ucneg 7751
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rex 2376  df-v 2635  df-un 3017  df-sn 3472  df-pr 3473  df-op 3475  df-uni 3676  df-br 3868  df-iota 5014  df-fv 5057  df-ov 5693  df-neg 7753
This theorem is referenced by:  negdi  7836  mulneg2  7971  mulm1  7975  eqord2  8059  mulreim  8178  apneg  8185  divnegap  8270  div2negap  8299  recgt0  8408  infrenegsupex  9181  supminfex  9184  ceilqval  9862  ceilid  9871  modqcyc2  9916  monoord2  10027  reneg  10417  imneg  10425  cjcj  10432  cjneg  10439  minmax  10776  minabs  10782  telfsumo2  11010  sinneg  11166  tannegap  11168  sincossq  11188  odd2np1  11300  oexpneg  11304  modgcd  11409  ex-ceil  12370
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