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Mirrors > Home > MPE Home > Th. List > s2len | Structured version Visualization version Unicode version |
Description: The length of a doubleton word. (Contributed by Stefan O'Rear, 23-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
s2len |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-s2 12980 |
. 2
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2 | s1cli 12778 |
. 2
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3 | s1len 12779 |
. 2
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4 | 1p1e2 10750 |
. 2
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5 | 1, 2, 3, 4 | cats1len 12992 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-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 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1457 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-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-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-en 7595 df-dom 7596 df-sdom 7597 df-fin 7598 df-card 8398 df-cda 8623 df-pnf 9702 df-mnf 9703 df-xr 9704 df-ltxr 9705 df-le 9706 df-sub 9887 df-neg 9888 df-nn 10637 df-2 10695 df-n0 10898 df-z 10966 df-uz 11188 df-fz 11813 df-fzo 11946 df-hash 12547 df-word 12696 df-concat 12698 df-s1 12699 df-s2 12980 |
This theorem is referenced by: s2dm 13020 s3fv0 13021 s3fv1 13022 s3fv2 13023 s3len 13024 lsws2 13034 s3tpop 13039 s4prop 13040 psgnunilem2 17184 efgtlen 17424 efgredleme 17441 efgredlemc 17443 frgpnabllem1 17557 lmat22lem 28691 lmat22e11 28692 lmat22e12 28693 lmat22e21 28694 lmat22e22 28695 lmat22det 28696 fiblem 29279 fib0 29280 fib1 29281 fibp1 29282 amgm2d 36693 pfx2 38992 11wlkdlem1 39851 1wlk2v2e 39871 21wlkdlem1 39873 21wlkdlem2 39874 21wlkdlem4 39876 2pthdlem1 39878 21wlkond 39885 2pthd 39888 2pthon3v-av 39891 umgr2adedgwlk 39893 |
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