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Mirrors > Home > ILE Home > Th. List > soinxp | Unicode version |
Description: Intersection of linear order with cross product of its field. (Contributed by Mario Carneiro, 10-Jul-2014.) |
Ref | Expression |
---|---|
soinxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | poinxp 4409 | . . 3 | |
2 | brinxp 4408 | . . . . . . . 8 | |
3 | 2 | 3adant3 924 | . . . . . . 7 |
4 | brinxp 4408 | . . . . . . . . 9 | |
5 | 4 | 3adant2 923 | . . . . . . . 8 |
6 | brinxp 4408 | . . . . . . . . . 10 | |
7 | 6 | ancoms 255 | . . . . . . . . 9 |
8 | 7 | 3adant1 922 | . . . . . . . 8 |
9 | 5, 8 | orbi12d 707 | . . . . . . 7 |
10 | 3, 9 | imbi12d 223 | . . . . . 6 |
11 | 10 | 3expb 1105 | . . . . 5 |
12 | 11 | 2ralbidva 2346 | . . . 4 |
13 | 12 | ralbiia 2338 | . . 3 |
14 | 1, 13 | anbi12i 433 | . 2 |
15 | df-iso 4034 | . 2 | |
16 | df-iso 4034 | . 2 | |
17 | 14, 15, 16 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 w3a 885 wcel 1393 wral 2306 cin 2916 class class class wbr 3764 wpo 4031 wor 4032 cxp 4343 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-po 4033 df-iso 4034 df-xp 4351 |
This theorem is referenced by: (None) |
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