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Theorem bj-minftynrr 36102
Description: The extended complex number -∞ is not a complex number. (Contributed by BJ, 27-Jun-2019.)
Assertion
Ref Expression
bj-minftynrr ¬ -∞ ∈ ℂ

Proof of Theorem bj-minftynrr
StepHypRef Expression
1 df-bj-minfty 36100 . 2 -∞ = (+∞ei‘π)
2 bj-inftyexpidisj 36086 . 2 ¬ (+∞ei‘π) ∈ ℂ
31, 2eqneltri 2852 1 ¬ -∞ ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2106  cfv 6543  cc 11107  πcpi 16009  +∞eicinftyexpi 36082  -∞cminfty 36099
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427  ax-un 7724  ax-reg 9586  ax-cnex 11165
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3or 1088  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2534  df-eu 2563  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-tp 4633  df-op 4635  df-uni 4909  df-br 5149  df-opab 5211  df-mpt 5232  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-dm 5686  df-iota 6495  df-fun 6545  df-fn 6546  df-fv 6551  df-c 11115  df-bj-inftyexpi 36083  df-bj-minfty 36100
This theorem is referenced by: (None)
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