Theorem nfnegd 8250

Description: Deduction version of nfneg 8251. (Contributed by NM, 29-Feb-2008.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypothesis

Ref	Expression
nfnegd.1	|- ( ph -> F/_ x A )

Assertion

Ref	Expression
nfnegd	|- ( ph -> F/_ x -u A )

Proof of Theorem nfnegd

Step	Hyp	Ref	Expression
1		df-neg 8228	. 2 |- -u A = ( 0 - A )
2		nfcvd 2348	. . 3 |- ( ph -> F/_ x 0 )
3		nfcvd 2348	. . 3 |- ( ph -> F/_ x - )
4		nfnegd.1	. . 3 |- ( ph -> F/_ x A )
5	2, 3, 4	nfovd 5963	. 2 |- ( ph -> F/_ x ( 0 - A ) )
6	1, 5	nfcxfrd 2345	1 |- ( ph -> F/_ x -u A )

Syntax hints:   -> wi 4   F/_wnfc 2334  (class class class)co 5934   0cc0 7907   - cmin 8225   -ucneg 8226

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-rex 2489  df-v 2773  df-un 3169  df-sn 3638  df-pr 3639  df-op 3641  df-uni 3850  df-br 4044  df-iota 5229  df-fv 5276  df-ov 5937  df-neg 8228

This theorem is referenced by:  nfneg  8251