Theorem nfneg 11348

Description: Bound-variable hypothesis builder for the negative of a complex number. (Contributed by NM, 12-Jun-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypothesis

Ref	Expression
nfneg.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfneg	⊢ Ⅎ𝑥-𝐴

Proof of Theorem nfneg

Step	Hyp	Ref	Expression
1		nfneg.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfnegd 11347	. 2 ⊢ (⊤ → Ⅎ𝑥-𝐴)
4	3	mptru 1548	1 ⊢ Ⅎ𝑥-𝐴

Syntax hints:  ⊤wtru 1542  Ⅎwnfc 2877  -cneg 11337

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-10 2143  ax-11 2159  ax-12 2179  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-ral 3046  df-rex 3055  df-rab 3394  df-v 3436  df-dif 3903  df-un 3905  df-ss 3917  df-nul 4282  df-if 4474  df-sn 4575  df-pr 4577  df-op 4581  df-uni 4858  df-br 5090  df-iota 6433  df-fv 6485  df-ov 7344  df-neg 11339

This theorem is referenced by:  riotaneg  12093  zriotaneg  12578  infcvgaux1i  15756  mbfposb  25574  dvfsum2  25961  infnsuprnmpt  45266  neglimc  45664  stoweidlem23  46040  stoweidlem47  46064