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Mirrors > Home > MPE Home > Th. List > 1lt3 | Structured version Visualization version Unicode version |
Description: 1 is less than 3. (Contributed by NM, 26-Sep-2010.) |
Ref | Expression |
---|---|
1lt3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1lt2 10776 |
. 2
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2 | 2lt3 10777 |
. 2
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3 | 1re 9642 |
. . 3
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4 | 2re 10679 |
. . 3
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5 | 3re 10683 |
. . 3
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6 | 3, 4, 5 | lttri 9760 |
. 2
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7 | 1, 2, 6 | mp2an 678 |
1
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Colors of variables: wff setvar class |
Syntax hints: class class
class wbr 4402 ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 ax-resscn 9596 ax-1cn 9597 ax-icn 9598 ax-addcl 9599 ax-addrcl 9600 ax-mulcl 9601 ax-mulrcl 9602 ax-mulcom 9603 ax-addass 9604 ax-mulass 9605 ax-distr 9606 ax-i2m1 9607 ax-1ne0 9608 ax-1rid 9609 ax-rnegex 9610 ax-rrecex 9611 ax-cnre 9612 ax-pre-lttri 9613 ax-pre-lttrn 9614 ax-pre-ltadd 9615 ax-pre-mulgt0 9616 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-po 4755 df-so 4756 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-riota 6252 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-er 7363 df-en 7570 df-dom 7571 df-sdom 7572 df-pnf 9677 df-mnf 9678 df-xr 9679 df-ltxr 9680 df-le 9681 df-sub 9862 df-neg 9863 df-2 10668 df-3 10669 |
This theorem is referenced by: 1le3 10826 fztpval 11857 expnass 12380 s4fv1 12990 f1oun2prg 13002 sin01gt0 14244 rpnnen2lem3 14269 rpnnen2lem9 14275 3prm 14641 6nprm 15081 7prm 15082 9nprm 15084 13prm 15087 19prm 15089 prmlem2 15091 37prm 15092 43prm 15093 139prm 15095 163prm 15096 631prm 15098 ressmulr 15250 opprbas 17857 matbas 19438 log2cnv 23870 cxploglim2 23904 dchrvmasumlem2 24336 pntibndlem1 24427 tgcgr4 24576 axlowdimlem16 24987 usgraexmpldifpr 25127 3v3e3cycl1 25372 constr3lem4 25375 constr3pthlem1 25383 konigsberg 25715 numclwlk1lem2f1 25822 frgraogt3nreg 25848 ex-dif 25873 ex-pss 25878 ex-res 25891 rabren3dioph 35658 jm2.23 35851 stoweidlem34 37895 stoweidlem42 37903 nnsum3primesprm 38885 nnsum4primesodd 38891 nnsum4primesoddALTV 38892 basendxnmulrndx 40007 |
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