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Theorem nfnegd 7981
 Description: Deduction version of nfneg 7982. (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 7959 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2283 . . 3 (𝜑𝑥0)
3 nfcvd 2283 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 5807 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2280 1 (𝜑𝑥-𝐴)
 Colors of variables: wff set class Syntax hints:   → wi 4  Ⅎwnfc 2269  (class class class)co 5781  0cc0 7643   − cmin 7956  -cneg 7957 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-iota 5095  df-fv 5138  df-ov 5784  df-neg 7959 This theorem is referenced by:  nfneg  7982
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