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Theorem nfnegd 9878
Description: Deduction version of nfneg 9879. (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 9871 . 2  |-  -u A  =  ( 0  -  A )
2 nfcvd 2581 . . 3  |-  ( ph  -> 
F/_ x 0 )
3 nfcvd 2581 . . 3  |-  ( ph  -> 
F/_ x  -  )
4 nfnegd.1 . . 3  |-  ( ph  -> 
F/_ x A )
52, 3, 4nfovd 6331 . 2  |-  ( ph  -> 
F/_ x ( 0  -  A ) )
61, 5nfcxfrd 2579 1  |-  ( ph  -> 
F/_ x -u A
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F/_wnfc 2566  (class class class)co 6306   0cc0 9547    - cmin 9868   -ucneg 9869
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-br 4424  df-iota 5565  df-fv 5609  df-ov 6309  df-neg 9871
This theorem is referenced by:  nfneg  9879
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