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Theorem bj-pinftynrr 33418
 Description: The extended complex number +∞ is not a complex number. (Contributed by BJ, 27-Jun-2019.)
Assertion
Ref Expression
bj-pinftynrr ¬ +∞ ∈ ℂ

Proof of Theorem bj-pinftynrr
StepHypRef Expression
1 bj-inftyexpidisj 33406 . 2 ¬ (inftyexpi ‘0) ∈ ℂ
2 df-bj-pinfty 33416 . . 3 +∞ = (inftyexpi ‘0)
32eleq1i 2828 . 2 (+∞ ∈ ℂ ↔ (inftyexpi ‘0) ∈ ℂ)
41, 3mtbir 312 1 ¬ +∞ ∈ ℂ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2137  ‘cfv 6047  ℂcc 10124  0cc0 10126  inftyexpi cinftyexpi 33402  +∞cpinfty 33415 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-8 2139  ax-9 2146  ax-10 2166  ax-11 2181  ax-12 2194  ax-13 2389  ax-ext 2738  ax-sep 4931  ax-nul 4939  ax-pow 4990  ax-pr 5053  ax-un 7112  ax-reg 8660  ax-cnex 10182 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3or 1073  df-3an 1074  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2045  df-eu 2609  df-mo 2610  df-clab 2745  df-cleq 2751  df-clel 2754  df-nfc 2889  df-ne 2931  df-ral 3053  df-rex 3054  df-rab 3057  df-v 3340  df-sbc 3575  df-dif 3716  df-un 3718  df-in 3720  df-ss 3727  df-nul 4057  df-if 4229  df-sn 4320  df-pr 4322  df-tp 4324  df-op 4326  df-uni 4587  df-br 4803  df-opab 4863  df-mpt 4880  df-id 5172  df-xp 5270  df-rel 5271  df-cnv 5272  df-co 5273  df-dm 5274  df-iota 6010  df-fun 6049  df-fn 6050  df-fv 6055  df-c 10132  df-bj-inftyexpi 33403  df-bj-pinfty 33416 This theorem is referenced by: (None)
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