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Theorem nfnegd 7599
Description: Deduction version of nfneg 7600. (Contributed by NM, 29-Feb-2008.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfnegd.1  |-  ( ph  -> 
F/_ x A )
Assertion
Ref Expression
nfnegd  |-  ( ph  -> 
F/_ x -u A
)

Proof of Theorem nfnegd
StepHypRef Expression
1 df-neg 7577 . 2  |-  -u A  =  ( 0  -  A )
2 nfcvd 2226 . . 3  |-  ( ph  -> 
F/_ x 0 )
3 nfcvd 2226 . . 3  |-  ( ph  -> 
F/_ x  -  )
4 nfnegd.1 . . 3  |-  ( ph  -> 
F/_ x A )
52, 3, 4nfovd 5616 . 2  |-  ( ph  -> 
F/_ x ( 0  -  A ) )
61, 5nfcxfrd 2223 1  |-  ( ph  -> 
F/_ x -u A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/_wnfc 2212  (class class class)co 5594   0cc0 7271    - cmin 7574   -ucneg 7575
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432  df-op 3434  df-uni 3631  df-br 3815  df-iota 4937  df-fv 4980  df-ov 5597  df-neg 7577
This theorem is referenced by:  nfneg  7600
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