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Theorem negeqi 7655
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 7654 . 2  |-  ( A  =  B  ->  -u A  =  -u B )
31, 2ax-mp 7 1  |-  -u A  =  -u B
Colors of variables: wff set class
Syntax hints:    = wceq 1289   -ucneg 7633
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3001  df-sn 3447  df-pr 3448  df-op 3450  df-uni 3649  df-br 3838  df-iota 4967  df-fv 5010  df-ov 5637  df-neg 7635
This theorem is referenced by:  negsubdii  7746  m1expcl2  9942  resqrexlemover  10408  resqrexlemcalc1  10412  absi  10457  geo2sum2  10870
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