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Theorem nfnegd 11454
Description: Deduction version of nfneg 11455. (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 11446 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2896 . . 3 (𝜑𝑥0)
3 nfcvd 2896 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 7431 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2894 1 (𝜑𝑥-𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnfc 2875  (class class class)co 7402  0cc0 11107  cmin 11443  -cneg 11444
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-neg 11446
This theorem is referenced by:  nfneg  11455  nfxnegd  44697
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