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Mirrors > Home > MPE Home > Th. List > 2lt3 | Structured version Visualization version Unicode version |
Description: 2 is less than 3. (Contributed by NM, 26-Sep-2010.) |
Ref | Expression |
---|---|
2lt3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2re 10679 |
. . 3
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2 | 1 | ltp1i 10510 |
. 2
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3 | df-3 10669 |
. 2
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4 | 2, 3 | breqtrri 4428 |
1
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Colors of variables: wff setvar class |
Syntax hints: class class
class wbr 4402 (class class class)co 6290
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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: 1lt3 10778 2lt4 10780 2lt6 10789 2lt7 10795 2lt8 10802 2lt9 10810 2lt10 10819 uzuzle23 11199 uz3m2nn 11201 fztpval 11857 expnass 12380 s4fv2 12991 f1oun2prg 13002 caucvgrlem 13736 caucvgrlemOLD 13737 cos01gt0 14245 3lcm2e6 14681 5prm 15080 11prm 15086 17prm 15088 23prm 15090 83prm 15094 317prm 15097 4001lem4 15115 rngstr 15244 oppradd 17858 cnfldstr 18972 matplusg 19439 log2le1 23876 chtub 24140 bpos1 24211 bposlem6 24217 chto1ub 24314 dchrvmasumiflem1 24339 istrkg3ld 24509 tgcgr4 24576 axlowdimlem2 24973 axlowdimlem16 24987 axlowdimlem17 24988 axlowdim 24991 usgraexmpldifpr 25127 3v3e3cycl1 25372 constr3lem4 25375 constr3trllem3 25380 constr3pthlem1 25383 constr3pthlem3 25385 konigsberg 25715 extwwlkfablem2 25806 ex-pss 25878 ex-res 25891 ex-fv 25893 ex-fl 25897 poimirlem9 31949 rabren3dioph 35658 jm2.20nn 35852 wallispilem4 37930 fourierdlem87 38057 nnsum3primes4 38883 nnsum3primesgbe 38887 nnsum3primesle9 38889 nnsum4primesodd 38891 nnsum4primesoddALTV 38892 tgoldbach 38911 plusgndxnmulrndx 40006 zlmodzxznm 40343 zlmodzxzldeplem 40344 3halfnz 40370 |
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