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Mirrors > Home > ILE Home > Th. List > poltletr | Unicode version |
Description: Transitive law for general strict orders. (Contributed by Stefan O'Rear, 17-Jan-2015.) |
Ref | Expression |
---|---|
poltletr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | poleloe 4933 | . . . . 5 | |
2 | 1 | 3ad2ant3 1004 | . . . 4 |
3 | 2 | adantl 275 | . . 3 |
4 | 3 | anbi2d 459 | . 2 |
5 | potr 4225 | . . . . 5 | |
6 | 5 | com12 30 | . . . 4 |
7 | breq2 3928 | . . . . . 6 | |
8 | 7 | biimpac 296 | . . . . 5 |
9 | 8 | a1d 22 | . . . 4 |
10 | 6, 9 | jaodan 786 | . . 3 |
11 | 10 | com12 30 | . 2 |
12 | 4, 11 | sylbid 149 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 697 w3a 962 wceq 1331 wcel 1480 cun 3064 class class class wbr 3924 cid 4205 wpo 4211 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-id 4210 df-po 4213 df-xp 4540 df-rel 4541 |
This theorem is referenced by: (None) |
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