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Theorem nfneg 10874
 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 𝑥𝐴
Assertion
Ref Expression
nfneg 𝑥-𝐴

Proof of Theorem nfneg
StepHypRef Expression
1 nfneg.1 . . . 4 𝑥𝐴
21a1i 11 . . 3 (⊤ → 𝑥𝐴)
32nfnegd 10873 . 2 (⊤ → 𝑥-𝐴)
43mptru 1545 1 𝑥-𝐴
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1539  Ⅎwnfc 2962  -cneg 10863 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 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4276  df-if 4450  df-sn 4550  df-pr 4552  df-op 4556  df-uni 4825  df-br 5053  df-iota 6302  df-fv 6351  df-ov 7148  df-neg 10865 This theorem is referenced by:  riotaneg  11612  zriotaneg  12089  infcvgaux1i  15208  mbfposb  24253  dvfsum2  24633  infnsuprnmpt  41750  neglimc  42152  stoweidlem23  42528  stoweidlem47  42552
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