Theorem negeqi 8268

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 8267	. 2 |- ( A = B -> -u A = -u B )
3	1, 2	ax-mp 5	1 |- -u A = -u B

Syntax hints:   = wceq 1373   -ucneg 8246

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-uni 3851  df-br 4046  df-iota 5233  df-fv 5280  df-ov 5949  df-neg 8248

This theorem is referenced by:  negsubdii  8359  m1expcl2  10708  resqrexlemover  11354  resqrexlemcalc1  11358  absi  11403  geo2sum2  11859  cos2bnd  12104  lgseisenlem1  15580  lgseisenlem2  15581  lgsquadlem1  15587