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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3697. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2744 | . 2 | |
2 | 3mix3 1163 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | abid 2158 | . . . . . 6 | |
5 | 3, 4 | syl6ibr 161 | . . . . 5 |
6 | dftp2 3630 | . . . . . 6 | |
7 | 6 | eleq2i 2237 | . . . . 5 |
8 | 5, 7 | syl6ibr 161 | . . . 4 |
9 | eleq1 2233 | . . . 4 | |
10 | 8, 9 | mpbidi 150 | . . 3 |
11 | 10 | exlimdv 1812 | . 2 |
12 | 1, 11 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 972 wceq 1348 wex 1485 wcel 2141 cab 2156 ctp 3583 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3or 974 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-tp 3589 |
This theorem is referenced by: rngmulrg 12522 srngmulrd 12529 lmodscad 12540 ipsmulrd 12548 ipsipd 12551 topgrptsetd 12558 |
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