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Mirrors > Home > ILE Home > Th. List > letri3d | Unicode version |
Description: Tightness of real apartness. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
ltd.1 | |
ltd.2 |
Ref | Expression |
---|---|
letri3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 | . 2 | |
2 | ltd.2 | . 2 | |
3 | letri3 7970 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 class class class wbr 3976 cr 7743 cle 7925 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-pre-ltirr 7856 ax-pre-apti 7859 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-pnf 7926 df-mnf 7927 df-xr 7928 df-ltxr 7929 df-le 7930 |
This theorem is referenced by: ltntri 8017 add20 8363 msq11 8788 squeeze0 8790 suprzclex 9280 exbtwnz 10176 flid 10209 expcan 10618 dfabsmax 11145 sumsnf 11336 prodsnf 11519 zssinfcl 11866 gcd0id 11897 gcdneg 11900 gcdaddm 11902 gcdzeq 11940 lcmneg 11985 coprmgcdb 11999 qredeq 12007 pw2dvdseu 12079 pcidlem 12233 pcgcd1 12238 refeq 13748 |
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