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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 |
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ltd.2 |
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Ref | Expression |
---|---|
letri3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 |
. 2
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2 | ltd.2 |
. 2
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3 | letri3 7762 |
. 2
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4 | 1, 2, 3 | syl2anc 406 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-setind 4410 ax-cnex 7630 ax-resscn 7631 ax-pre-ltirr 7651 ax-pre-apti 7654 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-fal 1318 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-nel 2376 df-ral 2393 df-rex 2394 df-rab 2397 df-v 2657 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-br 3894 df-opab 3948 df-xp 4503 df-cnv 4505 df-pnf 7720 df-mnf 7721 df-xr 7722 df-ltxr 7723 df-le 7724 |
This theorem is referenced by: ltntri 7807 add20 8149 msq11 8564 squeeze0 8566 suprzclex 9047 exbtwnz 9915 flid 9944 expcan 10350 dfabsmax 10875 sumsnf 11064 zssinfcl 11483 gcd0id 11509 gcdneg 11512 gcdaddm 11514 gcdzeq 11550 lcmneg 11595 coprmgcdb 11609 qredeq 11617 pw2dvdseu 11685 refeq 12904 |
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