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Mirrors > Home > ILE Home > Th. List > ltleletr | Unicode version |
Description: Transitive law, weaker
form of ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ltleletr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lttr 8062 |
. . . . . 6
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2 | 1 | 3coml 1212 |
. . . . 5
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3 | 2 | expcomd 1452 |
. . . 4
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4 | con3 643 |
. . . 4
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5 | 3, 4 | syl6 33 |
. . 3
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6 | lenlt 8064 |
. . . . 5
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7 | 6 | 3adant1 1017 |
. . . 4
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8 | lenlt 8064 |
. . . . 5
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9 | 8 | 3adant2 1018 |
. . . 4
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10 | 7, 9 | imbi12d 234 |
. . 3
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11 | 5, 10 | sylibrd 169 |
. 2
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12 | 11 | impd 254 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-setind 4554 ax-cnex 7933 ax-resscn 7934 ax-pre-lttrn 7956 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-pnf 8025 df-mnf 8026 df-xr 8027 df-ltxr 8028 df-le 8029 |
This theorem is referenced by: nn0ge2m1nn 9267 lbzbi 9648 iseqf1olemqk 10527 |
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