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Mirrors > Home > ILE Home > Th. List > eqleltd | Unicode version |
Description: Equality in terms of 'less than or equal to', 'less than'. (Contributed by NM, 7-Apr-2001.) |
Ref | Expression |
---|---|
ltd.1 | |
ltd.2 |
Ref | Expression |
---|---|
eqleltd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltd.1 | . 2 | |
2 | ltd.2 | . 2 | |
3 | eqlelt 7967 | . 2 | |
4 | 1, 2, 3 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wceq 1335 wcel 2128 class class class wbr 3967 cr 7734 clt 7915 cle 7916 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-pow 4138 ax-pr 4172 ax-un 4396 ax-setind 4499 ax-cnex 7826 ax-resscn 7827 ax-pre-ltirr 7847 ax-pre-apti 7850 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4029 df-xp 4595 df-cnv 4597 df-pnf 7917 df-mnf 7918 df-xr 7919 df-ltxr 7920 df-le 7921 |
This theorem is referenced by: pcpremul 12184 |
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