Theorem negeqi 7980

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

Step	Hyp	Ref	Expression
1		negeqi.1	. 2 |- A = B
2		negeq 7979	. 2 |- ( A = B -> -u A = -u B )
3	1, 2	ax-mp 5	1 |- -u A = -u B

Syntax hints:   = wceq 1332   -ucneg 7958

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-un 3080  df-sn 3538  df-pr 3539  df-op 3541  df-uni 3745  df-br 3938  df-iota 5096  df-fv 5139  df-ov 5785  df-neg 7960

This theorem is referenced by:  negsubdii  8071  m1expcl2  10346  resqrexlemover  10814  resqrexlemcalc1  10818  absi  10863  geo2sum2  11316  cos2bnd  11503