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Theorem bj-minftynrr 36628
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 36626 . 2 -∞ = (+∞ei‘π)
2 bj-inftyexpidisj 36612 . 2 ¬ (+∞ei‘π) ∈ ℂ
31, 2eqneltri 2847 1 ¬ -∞ ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2099  cfv 6542  cc 11122  πcpi 16028  +∞eicinftyexpi 36608  -∞cminfty 36625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2164  ax-ext 2698  ax-sep 5293  ax-nul 5300  ax-pr 5423  ax-un 7732  ax-reg 9601  ax-cnex 11180
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3or 1086  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2529  df-eu 2558  df-clab 2705  df-cleq 2719  df-clel 2805  df-nfc 2880  df-ne 2936  df-ral 3057  df-rex 3066  df-rab 3428  df-v 3471  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-tp 4629  df-op 4631  df-uni 4904  df-br 5143  df-opab 5205  df-mpt 5226  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-iota 6494  df-fun 6544  df-fn 6545  df-fv 6550  df-c 11130  df-bj-inftyexpi 36609  df-bj-minfty 36626
This theorem is referenced by: (None)
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