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Theorem nfneg 9709
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 9708 . 2  |-  ( T. 
->  F/_ x -u A
)
43trud 1379 1  |-  F/_ x -u A
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1371   F/_wnfc 2599   -ucneg 9699
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-uni 4192  df-br 4393  df-iota 5481  df-fv 5526  df-ov 6195  df-neg 9701
This theorem is referenced by:  riotaneg  10408  zriotaneg  10857  infcvgaux1i  13423  mbfposb  21249  dvfsum2  21624  stoweidlem23  29958  stoweidlem47  29982
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