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Theorem nfneg 10128
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 10127 . 2 (⊤ → 𝑥-𝐴)
43trud 1483 1 𝑥-𝐴
Colors of variables: wff setvar class
Syntax hints:  wtru 1475  wnfc 2737  -cneg 10118
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-br 4578  df-iota 5754  df-fv 5798  df-ov 6530  df-neg 10120
This theorem is referenced by:  riotaneg  10849  zriotaneg  11323  infcvgaux1i  14374  mbfposb  23143  dvfsum2  23518  neglimc  38511  stoweidlem23  38713  stoweidlem47  38737
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