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| Description: The number 8 is real. (Contributed by NM, 27-May-1999.) | 
| Ref | Expression | 
|---|---|
| 8re | ⊢ 8 ∈ ℝ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-8 12336 | . 2 ⊢ 8 = (7 + 1) | |
| 2 | 7re 12360 | . . 3 ⊢ 7 ∈ ℝ | |
| 3 | 1re 11262 | . . 3 ⊢ 1 ∈ ℝ | |
| 4 | 2, 3 | readdcli 11277 | . 2 ⊢ (7 + 1) ∈ ℝ | 
| 5 | 1, 4 | eqeltri 2836 | 1 ⊢ 8 ∈ ℝ | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∈ wcel 2107 (class class class)co 7432 ℝcr 11155 1c1 11157 + caddc 11159 7c7 12327 8c8 12328 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-1cn 11214 ax-icn 11215 ax-addcl 11216 ax-addrcl 11217 ax-mulcl 11218 ax-mulrcl 11219 ax-i2m1 11224 ax-1ne0 11225 ax-rrecex 11228 ax-cnre 11229 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-iota 6513 df-fv 6568 df-ov 7435 df-2 12330 df-3 12331 df-4 12332 df-5 12333 df-6 12334 df-7 12335 df-8 12336 | 
| This theorem is referenced by: 9re 12366 9pos 12380 6lt8 12460 5lt8 12461 4lt8 12462 3lt8 12463 2lt8 12464 1lt8 12465 8lt9 12466 7lt9 12467 8th4div3 12488 8lt10 12867 7lt10 12868 ef01bndlem 16221 cos2bnd 16225 slotstnscsi 17405 slotsdnscsi 17437 sralemOLD 21177 chtub 27257 bposlem8 27336 bposlem9 27337 lgsdir2lem1 27370 lgsdir2lem4 27373 lgsdir2lem5 27374 2lgsoddprmlem1 27453 2lgsoddprmlem2 27454 chebbnd1lem2 27515 chebbnd1lem3 27516 chebbnd1 27517 pntlemf 27650 cchhllemOLD 28903 hgt750lem 34667 hgt750lem2 34668 hgt750leme 34674 lcmineqlem23 42053 lcmineqlem 42054 3lexlogpow5ineq2 42057 aks4d1p1 42078 8rp 42342 resqrtvalex 43663 imsqrtvalex 43664 fmtnoprmfac2lem1 47558 mod42tp1mod8 47594 nnsum3primesle9 47786 nnsum4primesoddALTV 47789 nnsum4primesevenALTV 47793 bgoldbtbndlem1 47797 tgoldbach 47809 | 
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