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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-minftynrr | Structured version Visualization version GIF version |
Description: The extended complex number -∞ is not a complex number. (Contributed by BJ, 27-Jun-2019.) |
Ref | Expression |
---|---|
bj-minftynrr | ⊢ ¬ -∞ ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bj-minfty 35907 | . 2 ⊢ -∞ = (+∞ei‘π) | |
2 | bj-inftyexpidisj 35893 | . 2 ⊢ ¬ (+∞ei‘π) ∈ ℂ | |
3 | 1, 2 | eqneltri 2851 | 1 ⊢ ¬ -∞ ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2106 ‘cfv 6532 ℂcc 11090 πcpi 15992 +∞eicinftyexpi 35889 -∞cminfty 35906 |
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 2702 ax-sep 5292 ax-nul 5299 ax-pr 5420 ax-un 7708 ax-reg 9569 ax-cnex 11148 |
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 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3432 df-v 3475 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-if 4523 df-sn 4623 df-pr 4625 df-tp 4627 df-op 4629 df-uni 4902 df-br 5142 df-opab 5204 df-mpt 5225 df-id 5567 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-iota 6484 df-fun 6534 df-fn 6535 df-fv 6540 df-c 11098 df-bj-inftyexpi 35890 df-bj-minfty 35907 |
This theorem is referenced by: (None) |
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