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Theorem nfnegd 9047
Description: Deduction version of nfneg 9048. (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 9040 . 2  |-  -u A  =  ( 0  -  A )
2 nfcvd 2420 . . 3  |-  ( ph  -> 
F/_ x 0 )
3 nfcvd 2420 . . 3  |-  ( ph  -> 
F/_ x  -  )
4 nfnegd.1 . . 3  |-  ( ph  -> 
F/_ x A )
52, 3, 4nfovd 5880 . 2  |-  ( ph  -> 
F/_ x ( 0  -  A ) )
61, 5nfcxfrd 2417 1  |-  ( ph  -> 
F/_ x -u A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/_wnfc 2406  (class class class)co 5858   0cc0 8737    - cmin 9037   -ucneg 9038
This theorem is referenced by:  nfneg  9048
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861  df-neg 9040
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