Theorem nfneg 11380

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 11379	. 2 ⊢ (⊤ → Ⅎ𝑥-𝐴)
4	3	mptru 1549	1 ⊢ Ⅎ𝑥-𝐴

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  -cneg 11369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-ral 3053  df-rex 3062  df-rab 3401  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-if 4481  df-sn 4582  df-pr 4584  df-op 4588  df-uni 4865  df-br 5100  df-iota 6449  df-fv 6501  df-ov 7363  df-neg 11371

This theorem is referenced by:  riotaneg  12125  zriotaneg  12609  infcvgaux1i  15784  mbfposb  25614  dvfsum2  26001  infnsuprnmpt  45561  neglimc  45958  stoweidlem23  46334  stoweidlem47  46358