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Theorem nfnegd 9226
Description: Deduction version of nfneg 9227. (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 9219 . 2  |-  -u A  =  ( 0  -  A )
2 nfcvd 2517 . . 3  |-  ( ph  -> 
F/_ x 0 )
3 nfcvd 2517 . . 3  |-  ( ph  -> 
F/_ x  -  )
4 nfnegd.1 . . 3  |-  ( ph  -> 
F/_ x A )
52, 3, 4nfovd 6035 . 2  |-  ( ph  -> 
F/_ x ( 0  -  A ) )
61, 5nfcxfrd 2514 1  |-  ( ph  -> 
F/_ x -u A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/_wnfc 2503  (class class class)co 6013   0cc0 8916    - cmin 9216   -ucneg 9217
This theorem is referenced by:  nfneg  9227
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-uni 3951  df-br 4147  df-iota 5351  df-fv 5395  df-ov 6016  df-neg 9219
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