Theorem negeqi 8220

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

Step	Hyp	Ref	Expression
1		negeqi.1	. 2 ⊢ 𝐴 = 𝐵
2		negeq 8219	. 2 ⊢ (𝐴 = 𝐵 → -𝐴 = -𝐵)
3	1, 2	ax-mp 5	1 ⊢ -𝐴 = -𝐵

Syntax hints:   = wceq 1364  -cneg 8198

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-op 3631  df-uni 3840  df-br 4034  df-iota 5219  df-fv 5266  df-ov 5925  df-neg 8200

This theorem is referenced by:  negsubdii  8311  m1expcl2  10653  resqrexlemover  11175  resqrexlemcalc1  11179  absi  11224  geo2sum2  11680  cos2bnd  11925  lgseisenlem1  15311  lgseisenlem2  15312  lgsquadlem1  15318