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Mirrors > Home > ILE Home > Th. List > 2re | Unicode version |
Description: The number 2 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
2re |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8803 |
. 2
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2 | 1re 7789 |
. . 3
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3 | 2, 2 | readdcli 7803 |
. 2
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4 | 1, 3 | eqeltri 2213 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-ext 2122 ax-1re 7738 ax-addrcl 7741 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-clel 2136 df-2 8803 |
This theorem is referenced by: 2cn 8815 3re 8818 2ne0 8836 2ap0 8837 3pos 8838 2lt3 8914 1lt3 8915 2lt4 8917 1lt4 8918 2lt5 8921 2lt6 8926 1lt6 8927 2lt7 8932 1lt7 8933 2lt8 8939 1lt8 8940 2lt9 8947 1lt9 8948 1ap2 8951 1le2 8952 2rene0 8954 halfre 8957 halfgt0 8959 halflt1 8961 rehalfcl 8971 halfpos2 8974 halfnneg2 8976 addltmul 8980 nominpos 8981 avglt1 8982 avglt2 8983 div4p1lem1div2 8997 nn0lele2xi 9052 nn0ge2m1nn 9061 halfnz 9171 3halfnz 9172 2lt10 9343 1lt10 9344 eluz4eluz2 9389 uzuzle23 9393 uz3m2nn 9395 2rp 9475 xleaddadd 9700 fztpval 9894 fzo0to42pr 10028 qbtwnrelemcalc 10064 qbtwnre 10065 2tnp1ge0ge0 10105 flhalf 10106 fldiv4p1lem1div2 10109 mulp1mod1 10169 expubnd 10381 nn0opthlem2d 10499 faclbnd2 10520 4bc2eq6 10552 cvg1nlemres 10789 resqrexlemover 10814 resqrexlemga 10827 sqrt4 10851 sqrt2gt1lt2 10853 abstri 10908 amgm2 10922 maxabslemlub 11011 maxltsup 11022 bdtrilem 11042 efcllemp 11401 efcllem 11402 ege2le3 11414 ef01bndlem 11499 cos01bnd 11501 cos2bnd 11503 cos01gt0 11505 sin02gt0 11506 sincos2sgn 11508 sin4lt0 11509 cos12dec 11510 eirraplem 11519 egt2lt3 11522 epos 11523 ene1 11527 eap1 11528 oexpneg 11610 oddge22np1 11614 evennn02n 11615 evennn2n 11616 nn0ehalf 11636 nno 11639 nn0o 11640 nn0oddm1d2 11642 nnoddm1d2 11643 flodddiv4t2lthalf 11670 6gcd4e2 11719 ncoprmgcdne1b 11806 3lcm2e6 11874 sqrt2irrlem 11875 sqrt2re 11877 sqrt2irraplemnn 11893 sqrt2irrap 11894 plusgndxnmulrndx 12111 bl2in 12611 reeff1o 12902 cosz12 12909 sin0pilem1 12910 sin0pilem2 12911 pilem3 12912 pipos 12917 sinhalfpilem 12920 sincosq1lem 12954 sincosq4sgn 12958 sinq12gt0 12959 cosq23lt0 12962 coseq00topi 12964 coseq0negpitopi 12965 tangtx 12967 sincos4thpi 12969 tan4thpi 12970 sincos6thpi 12971 cosordlem 12978 cosq34lt1 12979 cos02pilt1 12980 cos0pilt1 12981 2logb9irr 13096 2logb3irr 13098 2logb9irrALT 13099 sqrt2cxp2logb9e3 13100 2logb9irrap 13102 ex-fl 13108 taupi 13430 |
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