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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 7564 |
. 2
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4 | 1, 2, 3 | syl2anc 403 |
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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-setind 4353 ax-cnex 7434 ax-resscn 7435 ax-pre-ltirr 7455 ax-pre-apti 7458 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-nel 2351 df-ral 2364 df-rex 2365 df-rab 2368 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-xp 4444 df-cnv 4446 df-pnf 7522 df-mnf 7523 df-xr 7524 df-ltxr 7525 df-le 7526 |
This theorem is referenced by: add20 7950 msq11 8361 squeeze0 8363 suprzclex 8842 exbtwnz 9658 flid 9687 expcan 10121 dfabsmax 10646 sumsnf 10799 zssinfcl 11218 gcd0id 11244 gcdneg 11247 gcdaddm 11249 gcdzeq 11285 lcmneg 11330 coprmgcdb 11344 qredeq 11352 pw2dvdseu 11420 |
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