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Mirrors > Home > ILE Home > Th. List > 10re | GIF version |
Description: The number 10 is real. (Contributed by NM, 5-Feb-2007.) (Revised by AV, 8-Sep-2021.) |
Ref | Expression |
---|---|
10re | ⊢ ;10 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 10nn 9397 | . 2 ⊢ ;10 ∈ ℕ | |
2 | 1 | nnrei 8926 | 1 ⊢ ;10 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 ℝcr 7809 0cc0 7810 1c1 7811 ;cdc 9382 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4121 ax-cnex 7901 ax-resscn 7902 ax-1cn 7903 ax-1re 7904 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-mulcom 7911 ax-addass 7912 ax-mulass 7913 ax-distr 7914 ax-1rid 7917 ax-0id 7918 ax-cnre 7921 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4004 df-iota 5178 df-fv 5224 df-ov 5877 df-inn 8918 df-2 8976 df-3 8977 df-4 8978 df-5 8979 df-6 8980 df-7 8981 df-8 8982 df-9 8983 df-dec 9383 |
This theorem is referenced by: 8lt10 9513 7lt10 9514 6lt10 9515 5lt10 9516 4lt10 9517 3lt10 9518 2lt10 9519 1lt10 9520 0.999... 11524 slotsdifdsndx 12670 slotsdifunifndx 12677 |
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