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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 4541 | . . 3 | |
2 | 1 | anbi2i 452 | . 2 |
3 | relssdmrn 5054 | . . . 4 | |
4 | ssv 3114 | . . . . 5 | |
5 | xpss12 4641 | . . . . 5 | |
6 | 4, 5 | mpan2 421 | . . . 4 |
7 | 3, 6 | sylan9ss 3105 | . . 3 |
8 | xpss 4642 | . . . . . 6 | |
9 | sstr 3100 | . . . . . 6 | |
10 | 8, 9 | mpan2 421 | . . . . 5 |
11 | df-rel 4541 | . . . . 5 | |
12 | 10, 11 | sylibr 133 | . . . 4 |
13 | dmss 4733 | . . . . 5 | |
14 | vn0m 3369 | . . . . . 6 | |
15 | dmxpm 4754 | . . . . . 6 | |
16 | 14, 15 | ax-mp 5 | . . . . 5 |
17 | 13, 16 | sseqtrdi 3140 | . . . 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 1331 wex 1468 wcel 1480 cvv 2681 wss 3066 cxp 4532 cdm 4534 crn 4535 wrel 4539 |
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 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-xp 4540 df-rel 4541 df-cnv 4542 df-dm 4544 df-rn 4545 |
This theorem is referenced by: dftpos3 6152 tpostpos2 6155 |
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