Theorem nfnegd 9878

Description: Deduction version of nfneg 9879. (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 9871	. 2 |- -u A = ( 0 - A )
2		nfcvd 2581	. . 3 |- ( ph -> F/_ x 0 )
3		nfcvd 2581	. . 3 |- ( ph -> F/_ x - )
4		nfnegd.1	. . 3 |- ( ph -> F/_ x A )
5	2, 3, 4	nfovd 6331	. 2 |- ( ph -> F/_ x ( 0 - A ) )
6	1, 5	nfcxfrd 2579	1 |- ( ph -> F/_ x -u A )

Syntax hints:   -> wi 4   F/_wnfc 2566  (class class class)co 6306   0cc0 9547   - cmin 9868   -ucneg 9869

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401

This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-br 4424  df-iota 5565  df-fv 5609  df-ov 6309  df-neg 9871

This theorem is referenced by:  nfneg  9879