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Theorem nfnegd 11504
Description: Deduction version of nfneg 11505. (Contributed by NM, 29-Feb-2008.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfnegd.1 (𝜑𝑥𝐴)
Assertion
Ref Expression
nfnegd (𝜑𝑥-𝐴)

Proof of Theorem nfnegd
StepHypRef Expression
1 df-neg 11496 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2905 . . 3 (𝜑𝑥0)
3 nfcvd 2905 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 7461 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2903 1 (𝜑𝑥-𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnfc 2889  (class class class)co 7432  0cc0 11156  cmin 11493  -cneg 11494
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-nf 1783  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4907  df-br 5143  df-iota 6513  df-fv 6568  df-ov 7435  df-neg 11496
This theorem is referenced by:  nfneg  11505  nfxnegd  45457
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