MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfneg Structured version   Unicode version

Theorem nfneg 9304
Description: Bound-variable hypothesis builder for the negative of a complex number. (Contributed by NM, 12-Jun-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfneg.1  |-  F/_ x A
Assertion
Ref Expression
nfneg  |-  F/_ x -u A

Proof of Theorem nfneg
StepHypRef Expression
1 nfneg.1 . . . 4  |-  F/_ x A
21a1i 11 . . 3  |-  (  T. 
->  F/_ x A )
32nfnegd 9303 . 2  |-  (  T. 
->  F/_ x -u A
)
43trud 1333 1  |-  F/_ x -u A
Colors of variables: wff set class
Syntax hints:    T. wtru 1326   F/_wnfc 2561   -ucneg 9294
This theorem is referenced by:  riotaneg  9985  infcvgaux1i  12638  mbfposb  19547  dvfsum2  19920  stoweidlem23  27750  stoweidlem47  27774
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-neg 9296
  Copyright terms: Public domain W3C validator