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Mirrors > Home > ILE Home > Th. List > 3re | Unicode version |
Description: The number 3 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
3re |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 8748 | . 2 | |
2 | 2re 8758 | . . 3 | |
3 | 1re 7733 | . . 3 | |
4 | 2, 3 | readdcli 7747 | . 2 |
5 | 1, 4 | 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 c3 8740 |
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 df-3 8748 |
This theorem is referenced by: 3cn 8763 4re 8765 3ne0 8783 3ap0 8784 4pos 8785 1lt3 8859 3lt4 8860 2lt4 8861 3lt5 8864 3lt6 8869 2lt6 8870 3lt7 8875 2lt7 8876 3lt8 8882 2lt8 8883 3lt9 8890 2lt9 8891 1le3 8899 8th4div3 8907 halfpm6th 8908 3halfnz 9116 3lt10 9286 2lt10 9287 uzuzle23 9334 uz3m2nn 9336 nn01to3 9377 3rp 9415 expnass 10366 sqrt9 10788 ef01bndlem 11390 sin01bnd 11391 cos2bnd 11394 sin01gt0 11395 cos01gt0 11396 egt2lt3 11413 flodddiv4 11558 dveflem 12782 sincosq3sgn 12836 sincosq4sgn 12837 cosq23lt0 12841 coseq0q4123 12842 coseq00topi 12843 coseq0negpitopi 12844 tangtx 12846 sincos6thpi 12850 pigt3 12852 pige3 12853 cos02pilt1 12859 ex-fl 12864 ex-gcd 12870 |
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