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Mirrors > Home > MPE Home > Th. List > 6re | Structured version Visualization version GIF version |
Description: The number 6 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
6re | ⊢ 6 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-6 11692 | . 2 ⊢ 6 = (5 + 1) | |
2 | 5re 11712 | . . 3 ⊢ 5 ∈ ℝ | |
3 | 1re 10629 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 10644 | . 2 ⊢ (5 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2906 | 1 ⊢ 6 ∈ ℝ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 (class class class)co 7145 ℝcr 10524 1c1 10526 + caddc 10528 5c5 11683 6c6 11684 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-1cn 10583 ax-icn 10584 ax-addcl 10585 ax-addrcl 10586 ax-mulcl 10587 ax-mulrcl 10588 ax-i2m1 10593 ax-1ne0 10594 ax-rrecex 10597 ax-cnre 10598 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-2 11688 df-3 11689 df-4 11690 df-5 11691 df-6 11692 |
This theorem is referenced by: 7re 11718 7pos 11736 4lt6 11807 3lt6 11808 2lt6 11809 1lt6 11810 6lt7 11811 5lt7 11812 6lt8 11818 5lt8 11819 6lt9 11826 5lt9 11827 8th4div3 11845 halfpm6th 11846 div4p1lem1div2 11880 6lt10 12220 5lt10 12221 5recm6rec 12230 bpoly2 15399 bpoly3 15400 efi4p 15478 resin4p 15479 recos4p 15480 ef01bndlem 15525 sin01bnd 15526 cos01bnd 15527 lt6abl 18944 sralem 19878 sravsca 19883 zlmlem 20592 sincos6thpi 25028 pigt3 25030 basellem5 25589 basellem8 25592 basellem9 25593 ppiublem1 25705 ppiublem2 25706 ppiub 25707 chtub 25715 bposlem6 25792 bposlem8 25794 ex-res 28147 zlmds 31104 zlmtset 31105 hgt750lemd 31818 hgt750lem2 31822 hgt750leme 31828 problem4 32808 problem5 32809 gbegt5 43803 gbowgt5 43804 gbowge7 43805 gboge9 43806 sbgoldbwt 43819 sgoldbeven3prm 43825 mogoldbb 43827 sbgoldbo 43829 nnsum3primesle9 43836 nnsum4primesodd 43838 wtgoldbnnsum4prm 43844 bgoldbnnsum3prm 43846 pgrple2abl 44341 |
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