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Theorem nfnegd 7625
Description: Deduction version of nfneg 7626. (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 7603 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2226 . . 3 (𝜑𝑥0)
3 nfcvd 2226 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 5637 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2223 1 (𝜑𝑥-𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wnfc 2212  (class class class)co 5615  0cc0 7297  cmin 7600  -cneg 7601
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3639  df-br 3823  df-iota 4948  df-fv 4991  df-ov 5618  df-neg 7603
This theorem is referenced by:  nfneg  7626
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