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Theorem negeqi 7737
Description: Equality inference for negatives. (Contributed by NM, 14-Feb-1995.)
Hypothesis
Ref Expression
negeqi.1 𝐴 = 𝐵
Assertion
Ref Expression
negeqi -𝐴 = -𝐵

Proof of Theorem negeqi
StepHypRef Expression
1 negeqi.1 . 2 𝐴 = 𝐵
2 negeq 7736 . 2 (𝐴 = 𝐵 → -𝐴 = -𝐵)
31, 2ax-mp 7 1 -𝐴 = -𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1290  -cneg 7715
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 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2622  df-un 3004  df-sn 3456  df-pr 3457  df-op 3459  df-uni 3660  df-br 3852  df-iota 4993  df-fv 5036  df-ov 5669  df-neg 7717
This theorem is referenced by:  negsubdii  7828  m1expcl2  10038  resqrexlemover  10504  resqrexlemcalc1  10508  absi  10553  geo2sum2  10970  cos2bnd  11112
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