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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 4643 | . . . 4 | |
2 | df-br 3990 | . . . 4 | |
3 | 1, 2 | sylibr 133 | . . 3 |
4 | swoer.1 | . . . . . 6 | |
5 | 4 | breqi 3995 | . . . . 5 |
6 | brdif 4042 | . . . . 5 | |
7 | 5, 6 | bitri 183 | . . . 4 |
8 | 7 | baib 914 | . . 3 |
9 | 3, 8 | syl 14 | . 2 |
10 | brun 4040 | . . . 4 | |
11 | brcnvg 4792 | . . . . 5 | |
12 | 11 | orbi2d 785 | . . . 4 |
13 | 10, 12 | syl5bb 191 | . . 3 |
14 | 13 | notbid 662 | . 2 |
15 | 9, 14 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 703 wceq 1348 wcel 2141 cdif 3118 cun 3119 cop 3586 class class class wbr 3989 cxp 4609 ccnv 4610 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-cnv 4619 |
This theorem is referenced by: swoer 6541 swoord1 6542 swoord2 6543 |
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