Theorem nfneg 11428

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 11427	. 2 ⊢ (⊤ → Ⅎ𝑥-𝐴)
4	3	mptru 1569	1 ⊢ Ⅎ𝑥-𝐴

Syntax hints:  ⊤wtru 1563  Ⅎwnfc 2911  -cneg 11417

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2214  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1565  df-fal 1575  df-ex 1802  df-nf 1806  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-nfc 2913  df-ral 3079  df-rex 3089  df-rab 3417  df-v 3458  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4288  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5103  df-iota 6479  df-fv 6531  df-ov 7401  df-neg 11419

This theorem is referenced by:  riotaneg  12173  zriotaneg  12688  infcvgaux1i  15889  mbfposb  25717  dvfsum2  26098  infnsuprnmpt  45830  neglimc  46226  stoweidlem23  46602  stoweidlem47  46626