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Mirrors > Home > MPE Home > Th. List > epos | Structured version Visualization version Unicode version |
Description: Euler's constant ![]() |
Ref | Expression |
---|---|
epos |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2pos 10728 |
. 2
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2 | egt2lt3 14306 |
. . 3
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3 | 2 | simpli 464 |
. 2
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4 | 0re 9668 |
. . 3
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5 | 2re 10706 |
. . 3
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6 | ere 14191 |
. . 3
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7 | 4, 5, 6 | lttri 9785 |
. 2
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8 | 1, 3, 7 | mp2an 683 |
1
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Colors of variables: wff setvar class |
Syntax hints: class class
class wbr 4415 ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-rep 4528 ax-sep 4538 ax-nul 4547 ax-pow 4594 ax-pr 4652 ax-un 6609 ax-inf2 8171 ax-cnex 9620 ax-resscn 9621 ax-1cn 9622 ax-icn 9623 ax-addcl 9624 ax-addrcl 9625 ax-mulcl 9626 ax-mulrcl 9627 ax-mulcom 9628 ax-addass 9629 ax-mulass 9630 ax-distr 9631 ax-i2m1 9632 ax-1ne0 9633 ax-1rid 9634 ax-rnegex 9635 ax-rrecex 9636 ax-cnre 9637 ax-pre-lttri 9638 ax-pre-lttrn 9639 ax-pre-ltadd 9640 ax-pre-mulgt0 9641 ax-pre-sup 9642 ax-addf 9643 ax-mulf 9644 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1457 df-fal 1460 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-nel 2635 df-ral 2753 df-rex 2754 df-reu 2755 df-rmo 2756 df-rab 2757 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-pss 3431 df-nul 3743 df-if 3893 df-pw 3964 df-sn 3980 df-pr 3982 df-tp 3984 df-op 3986 df-uni 4212 df-int 4248 df-iun 4293 df-br 4416 df-opab 4475 df-mpt 4476 df-tr 4511 df-eprel 4763 df-id 4767 df-po 4773 df-so 4774 df-fr 4811 df-se 4812 df-we 4813 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 df-pred 5398 df-ord 5444 df-on 5445 df-lim 5446 df-suc 5447 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-isom 5609 df-riota 6276 df-ov 6317 df-oprab 6318 df-mpt2 6319 df-om 6719 df-1st 6819 df-2nd 6820 df-wrecs 7053 df-recs 7115 df-rdg 7153 df-1o 7207 df-oadd 7211 df-er 7388 df-pm 7500 df-en 7595 df-dom 7596 df-sdom 7597 df-fin 7598 df-sup 7981 df-inf 7982 df-oi 8050 df-card 8398 df-pnf 9702 df-mnf 9703 df-xr 9704 df-ltxr 9705 df-le 9706 df-sub 9887 df-neg 9888 df-div 10297 df-nn 10637 df-2 10695 df-3 10696 df-4 10697 df-n0 10898 df-z 10966 df-uz 11188 df-q 11293 df-rp 11331 df-ico 11669 df-fz 11813 df-fzo 11946 df-fl 12059 df-seq 12245 df-exp 12304 df-fac 12491 df-bc 12519 df-hash 12547 df-shft 13178 df-cj 13210 df-re 13211 df-im 13212 df-sqrt 13346 df-abs 13347 df-limsup 13574 df-clim 13600 df-rlim 13601 df-sum 13801 df-ef 14169 df-e 14170 |
This theorem is referenced by: epr 14308 ene0 14309 logdivlti 23617 logdivlt 23618 logdivle 23619 ecxp 23666 bposlem7 24266 bposlem9 24268 chebbnd1lem3 24357 chebbnd1 24358 logdivsum 24419 subfaclim 29959 subfacval3 29960 stirlinglem3 37975 stirlinglem4 37976 stirlinglem13 37985 stirlinglem14 37986 stirlinglem15 37987 stirlingr 37989 etransclem23 38159 etransclem46 38182 |
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