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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3609. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2674 | . 2 | |
2 | 3mix3 1137 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | abid 2105 | . . . . . 6 | |
5 | 3, 4 | syl6ibr 161 | . . . . 5 |
6 | dftp2 3542 | . . . . . 6 | |
7 | 6 | eleq2i 2184 | . . . . 5 |
8 | 5, 7 | syl6ibr 161 | . . . 4 |
9 | eleq1 2180 | . . . 4 | |
10 | 8, 9 | mpbidi 150 | . . 3 |
11 | 10 | exlimdv 1775 | . 2 |
12 | 1, 11 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 946 wceq 1316 wex 1453 wcel 1465 cab 2103 ctp 3499 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-tp 3505 |
This theorem is referenced by: rngmulrg 12004 srngmulrd 12011 lmodscad 12022 ipsmulrd 12030 ipsipd 12033 topgrptsetd 12040 |
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