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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3639. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2700 | . 2 | |
2 | 3mix3 1152 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | abid 2127 | . . . . . 6 | |
5 | 3, 4 | syl6ibr 161 | . . . . 5 |
6 | dftp2 3572 | . . . . . 6 | |
7 | 6 | eleq2i 2206 | . . . . 5 |
8 | 5, 7 | syl6ibr 161 | . . . 4 |
9 | eleq1 2202 | . . . 4 | |
10 | 8, 9 | mpbidi 150 | . . 3 |
11 | 10 | exlimdv 1791 | . 2 |
12 | 1, 11 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 961 wceq 1331 wex 1468 wcel 1480 cab 2125 ctp 3529 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-tp 3535 |
This theorem is referenced by: rngmulrg 12080 srngmulrd 12087 lmodscad 12098 ipsmulrd 12106 ipsipd 12109 topgrptsetd 12116 |
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