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Theorem nfneg 7582
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 9 . . 3  |-  ( T. 
->  F/_ x A )
32nfnegd 7581 . 2  |-  ( T. 
->  F/_ x -u A
)
43trud 1294 1  |-  F/_ x -u A
Colors of variables: wff set class
Syntax hints:   T. wtru 1286   F/_wnfc 2210   -ucneg 7557
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-v 2614  df-un 2988  df-sn 3428  df-pr 3429  df-op 3431  df-uni 3628  df-br 3812  df-iota 4934  df-fv 4977  df-ov 5594  df-neg 7559
This theorem is referenced by:  infssuzcldc  10727
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