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Theorem nfnegd 10617
 Description: Deduction version of nfneg 10618. (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 10609 . 2 -𝐴 = (0 − 𝐴)
2 nfcvd 2935 . . 3 (𝜑𝑥0)
3 nfcvd 2935 . . 3 (𝜑𝑥 − )
4 nfnegd.1 . . 3 (𝜑𝑥𝐴)
52, 3, 4nfovd 6951 . 2 (𝜑𝑥(0 − 𝐴))
61, 5nfcxfrd 2933 1 (𝜑𝑥-𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnfc 2919  (class class class)co 6922  0cc0 10272   − cmin 10606  -cneg 10607 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-ral 3095  df-rex 3096  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-uni 4672  df-br 4887  df-iota 6099  df-fv 6143  df-ov 6925  df-neg 10609 This theorem is referenced by:  nfneg  10618  nfxnegd  40578
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