Theorem nfnegd 9901

Description: Deduction version of nfneg 9902. (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 9894	. 2 |- -u A = ( 0 - A )
2		nfcvd 2604	. . 3 |- ( ph -> F/_ x 0 )
3		nfcvd 2604	. . 3 |- ( ph -> F/_ x - )
4		nfnegd.1	. . 3 |- ( ph -> F/_ x A )
5	2, 3, 4	nfovd 6345	. 2 |- ( ph -> F/_ x ( 0 - A ) )
6	1, 5	nfcxfrd 2602	1 |- ( ph -> F/_ x -u A )

Syntax hints:   -> wi 4   F/_wnfc 2590  (class class class)co 6320   0cc0 9570   - cmin 9891   -ucneg 9892

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442

This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-3an 993  df-tru 1458  df-ex 1675  df-nf 1679  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592  df-ral 2754  df-rex 2755  df-rab 2758  df-v 3059  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3744  df-if 3894  df-sn 3981  df-pr 3983  df-op 3987  df-uni 4213  df-br 4419  df-iota 5569  df-fv 5613  df-ov 6323  df-neg 9894

This theorem is referenced by:  nfneg  9902