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Theorem nfnegd 11317
Description: Deduction version of nfneg 11318. (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 11309 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2905 . . 3 (𝜑𝑥0)
3 nfcvd 2905 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 7366 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2903 1 (𝜑𝑥-𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnfc 2884  (class class class)co 7337  0cc0 10972  cmin 11306  -cneg 11307
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2886  df-ral 3062  df-rex 3071  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4270  df-if 4474  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4853  df-br 5093  df-iota 6431  df-fv 6487  df-ov 7340  df-neg 11309
This theorem is referenced by:  nfneg  11318  nfxnegd  43324
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