Theorem nfnegd 8094

Description: Deduction version of nfneg 8095. (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 8072	. 2 |- -u A = ( 0 - A )
2		nfcvd 2309	. . 3 |- ( ph -> F/_ x 0 )
3		nfcvd 2309	. . 3 |- ( ph -> F/_ x - )
4		nfnegd.1	. . 3 |- ( ph -> F/_ x A )
5	2, 3, 4	nfovd 5871	. 2 |- ( ph -> F/_ x ( 0 - A ) )
6	1, 5	nfcxfrd 2306	1 |- ( ph -> F/_ x -u A )

Syntax hints:   -> wi 4   F/_wnfc 2295  (class class class)co 5842   0cc0 7753   - cmin 8069   -ucneg 8070

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-op 3585  df-uni 3790  df-br 3983  df-iota 5153  df-fv 5196  df-ov 5845  df-neg 8072

This theorem is referenced by:  nfneg  8095