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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3506. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2613 | . 2 | |
2 | 3mix3 1109 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | abid 2069 | . . . . . 6 | |
5 | 3, 4 | syl6ibr 160 | . . . . 5 |
6 | dftp2 3441 | . . . . . 6 | |
7 | 6 | eleq2i 2145 | . . . . 5 |
8 | 5, 7 | syl6ibr 160 | . . . 4 |
9 | eleq1 2141 | . . . 4 | |
10 | 8, 9 | mpbidi 149 | . . 3 |
11 | 10 | exlimdv 1740 | . 2 |
12 | 1, 11 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 918 wceq 1284 wex 1421 wcel 1433 cab 2067 ctp 3400 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-tp 3406 |
This theorem is referenced by: (None) |
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