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Theorem bj-minftynrr 37227
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 37225 . 2 -∞ = (+∞ei‘π)
2 bj-inftyexpidisj 37211 . 2 ¬ (+∞ei‘π) ∈ ℂ
31, 2eqneltri 2860 1 ¬ -∞ ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2108  cfv 6561  cc 11153  πcpi 16102  +∞eicinftyexpi 37207  -∞cminfty 37224
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432  ax-un 7755  ax-reg 9632  ax-cnex 11211
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-tp 4631  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-mpt 5226  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-co 5694  df-dm 5695  df-iota 6514  df-fun 6563  df-fn 6564  df-fv 6569  df-c 11161  df-bj-inftyexpi 37208  df-bj-minfty 37225
This theorem is referenced by: (None)
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