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Mirrors > Home > ILE Home > Th. List > brdifun | Unicode version |
Description: Evaluate the incomparability relation. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
swoer.1 |
Ref | Expression |
---|---|
brdifun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4619 | . . . 4 | |
2 | df-br 3967 | . . . 4 | |
3 | 1, 2 | sylibr 133 | . . 3 |
4 | swoer.1 | . . . . . 6 | |
5 | 4 | breqi 3972 | . . . . 5 |
6 | brdif 4018 | . . . . 5 | |
7 | 5, 6 | bitri 183 | . . . 4 |
8 | 7 | baib 905 | . . 3 |
9 | 3, 8 | syl 14 | . 2 |
10 | brun 4016 | . . . 4 | |
11 | brcnvg 4768 | . . . . 5 | |
12 | 11 | orbi2d 780 | . . . 4 |
13 | 10, 12 | syl5bb 191 | . . 3 |
14 | 13 | notbid 657 | . 2 |
15 | 9, 14 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 698 wceq 1335 wcel 2128 cdif 3099 cun 3100 cop 3563 class class class wbr 3966 cxp 4585 ccnv 4586 |
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-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 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-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-xp 4593 df-cnv 4595 |
This theorem is referenced by: swoer 6509 swoord1 6510 swoord2 6511 |
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