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Mirrors > Home > ILE Home > Th. List > tpostpos2 | Unicode version |
Description: Value of the double transposition for a relation on triples. (Contributed by Mario Carneiro, 16-Sep-2015.) |
Ref | Expression |
---|---|
tpostpos2 | tpos tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tpostpos 6213 | . 2 tpos tpos | |
2 | relrelss 5114 | . . . 4 | |
3 | ssun1 3271 | . . . . . 6 | |
4 | xpss1 4698 | . . . . . 6 | |
5 | 3, 4 | ax-mp 5 | . . . . 5 |
6 | sstr 3136 | . . . . 5 | |
7 | 5, 6 | mpan2 422 | . . . 4 |
8 | 2, 7 | sylbi 120 | . . 3 |
9 | df-ss 3115 | . . 3 | |
10 | 8, 9 | sylib 121 | . 2 |
11 | 1, 10 | syl5eq 2202 | 1 tpos tpos |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 cvv 2712 cun 3100 cin 3101 wss 3102 c0 3395 csn 3561 cxp 4586 cdm 4588 wrel 4593 tpos ctpos 6193 |
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-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-nul 4092 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 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-ne 2328 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-fv 5180 df-tpos 6194 |
This theorem is referenced by: (None) |
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