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Mirrors > Home > ILE Home > Th. List > relrelss | Unicode version |
Description: Two ways to describe the structure of a two-place operation. (Contributed by NM, 17-Dec-2008.) |
Ref | Expression |
---|---|
relrelss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel 4605 | . . 3 | |
2 | 1 | anbi2i 453 | . 2 |
3 | relssdmrn 5118 | . . . 4 | |
4 | ssv 3159 | . . . . 5 | |
5 | xpss12 4705 | . . . . 5 | |
6 | 4, 5 | mpan2 422 | . . . 4 |
7 | 3, 6 | sylan9ss 3150 | . . 3 |
8 | xpss 4706 | . . . . . 6 | |
9 | sstr 3145 | . . . . . 6 | |
10 | 8, 9 | mpan2 422 | . . . . 5 |
11 | df-rel 4605 | . . . . 5 | |
12 | 10, 11 | sylibr 133 | . . . 4 |
13 | dmss 4797 | . . . . 5 | |
14 | vn0m 3415 | . . . . . 6 | |
15 | dmxpm 4818 | . . . . . 6 | |
16 | 14, 15 | ax-mp 5 | . . . . 5 |
17 | 13, 16 | sseqtrdi 3185 | . . . 4 |
18 | 12, 17 | jca 304 | . . 3 |
19 | 7, 18 | impbii 125 | . 2 |
20 | 2, 19 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 cvv 2721 wss 3111 cxp 4596 cdm 4598 crn 4599 wrel 4603 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 df-dm 4608 df-rn 4609 |
This theorem is referenced by: dftpos3 6221 tpostpos2 6224 |
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