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Theorem nfnegd 6984
Description: Deduction version of nfneg 6985. (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 6962 . 2 -A = (0 − A)
2 nfcvd 2176 . . 3 (φx0)
3 nfcvd 2176 . . 3 (φx − )
4 nfnegd.1 . . 3 (φxA)
52, 3, 4nfovd 5477 . 2 (φx(0 − A))
61, 5nfcxfrd 2173 1 (φx-A)
Colors of variables: wff set class
Syntax hints:  wi 4  wnfc 2162  (class class class)co 5455  0cc0 6691  cmin 6959  -cneg 6960
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458  df-neg 6962
This theorem is referenced by:  nfneg  6985
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