Theorem negeqi 8467

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 8466	. 2 |- ( A = B -> -u A = -u B )
3	1, 2	ax-mp 5	1 |- -u A = -u B

Syntax hints:   = wceq 1398   -ucneg 8445

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rex 2526  df-v 2815  df-un 3215  df-sn 3695  df-pr 3696  df-op 3698  df-uni 3915  df-br 4110  df-iota 5312  df-fv 5360  df-ov 6053  df-neg 8447

This theorem is referenced by:  negsubdii  8558  m1expcl2  10923  resqrexlemover  11695  resqrexlemcalc1  11699  absi  11744  geo2sum2  12201  cos2bnd  12446  ballotfilem2  13142  lgseisenlem1  15943  lgseisenlem2  15944  lgsquadlem1  15950