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Theorem bj-pinftynrr 33420
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 33408 . 2 ¬ (inftyexpi ‘0) ∈ ℂ
2 df-bj-pinfty 33418 . . 3 +∞ = (inftyexpi ‘0)
32eleq1i 2830 . 2 (+∞ ∈ ℂ ↔ (inftyexpi ‘0) ∈ ℂ)
41, 3mtbir 312 1 ¬ +∞ ∈ ℂ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2139  cfv 6049  cc 10126  0cc0 10128  inftyexpi cinftyexpi 33404  +∞cpinfty 33417
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-8 2141  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pow 4992  ax-pr 5055  ax-un 7114  ax-reg 8662  ax-cnex 10184
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3or 1073  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ne 2933  df-ral 3055  df-rex 3056  df-rab 3059  df-v 3342  df-sbc 3577  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-tp 4326  df-op 4328  df-uni 4589  df-br 4805  df-opab 4865  df-mpt 4882  df-id 5174  df-xp 5272  df-rel 5273  df-cnv 5274  df-co 5275  df-dm 5276  df-iota 6012  df-fun 6051  df-fn 6052  df-fv 6057  df-c 10134  df-bj-inftyexpi 33405  df-bj-pinfty 33418
This theorem is referenced by: (None)
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