Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2re | Unicode version |
Description: The number 2 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2re |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8747 | . 2 | |
2 | 1re 7733 | . . 3 | |
3 | 2, 2 | readdcli 7747 | . 2 |
4 | 1, 3 | eqeltri 2190 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 (class class class)co 5742 cr 7587 c1 7589 caddc 7591 c2 8739 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-2 8747 |
This theorem is referenced by: 2cn 8759 3re 8762 2ne0 8780 2ap0 8781 3pos 8782 2lt3 8858 1lt3 8859 2lt4 8861 1lt4 8862 2lt5 8865 2lt6 8870 1lt6 8871 2lt7 8876 1lt7 8877 2lt8 8883 1lt8 8884 2lt9 8891 1lt9 8892 1ap2 8895 1le2 8896 2rene0 8898 halfre 8901 halfgt0 8903 halflt1 8905 rehalfcl 8915 halfpos2 8918 halfnneg2 8920 addltmul 8924 nominpos 8925 avglt1 8926 avglt2 8927 div4p1lem1div2 8941 nn0lele2xi 8996 nn0ge2m1nn 9005 halfnz 9115 3halfnz 9116 2lt10 9287 1lt10 9288 uzuzle23 9334 uz3m2nn 9336 2rp 9414 xleaddadd 9638 fztpval 9831 fzo0to42pr 9965 qbtwnrelemcalc 10001 qbtwnre 10002 2tnp1ge0ge0 10042 flhalf 10043 fldiv4p1lem1div2 10046 mulp1mod1 10106 expubnd 10318 nn0opthlem2d 10435 faclbnd2 10456 4bc2eq6 10488 cvg1nlemres 10725 resqrexlemover 10750 resqrexlemga 10763 sqrt4 10787 sqrt2gt1lt2 10789 abstri 10844 amgm2 10858 maxabslemlub 10947 maxltsup 10958 bdtrilem 10978 efcllemp 11291 efcllem 11292 ege2le3 11304 ef01bndlem 11390 cos01bnd 11392 cos2bnd 11394 cos01gt0 11396 sin02gt0 11397 sincos2sgn 11399 sin4lt0 11400 cos12dec 11401 eirraplem 11410 egt2lt3 11413 epos 11414 ene1 11418 eap1 11419 oexpneg 11501 oddge22np1 11505 evennn02n 11506 evennn2n 11507 nn0ehalf 11527 nno 11530 nn0o 11531 nn0oddm1d2 11533 nnoddm1d2 11534 flodddiv4t2lthalf 11561 6gcd4e2 11610 ncoprmgcdne1b 11697 3lcm2e6 11765 sqrt2irrlem 11766 sqrt2re 11768 sqrt2irraplemnn 11784 sqrt2irrap 11785 plusgndxnmulrndx 11999 bl2in 12499 cosz12 12788 sin0pilem1 12789 sin0pilem2 12790 pilem3 12791 pipos 12796 sinhalfpilem 12799 sincosq1lem 12833 sincosq4sgn 12837 sinq12gt0 12838 cosq23lt0 12841 coseq00topi 12843 coseq0negpitopi 12844 tangtx 12846 sincos4thpi 12848 tan4thpi 12849 sincos6thpi 12850 cosordlem 12857 cosq34lt1 12858 cos02pilt1 12859 ex-fl 12864 taupi 13166 |
Copyright terms: Public domain | W3C validator |