Theorem negeqi 8432

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 8431	. 2 |- ( A = B -> -u A = -u B )
3	1, 2	ax-mp 5	1 |- -u A = -u B

Syntax hints:   = wceq 1398   -ucneg 8410

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 2213

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-op 3682  df-uni 3899  df-br 4094  df-iota 5293  df-fv 5341  df-ov 6031  df-neg 8412

This theorem is referenced by:  negsubdii  8523  m1expcl2  10886  resqrexlemover  11650  resqrexlemcalc1  11654  absi  11699  geo2sum2  12156  cos2bnd  12401  lgseisenlem1  15889  lgseisenlem2  15890  lgsquadlem1  15896