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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3484. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . 2 | |
2 | 3mix3 1075 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | abid 2028 | . . . . . 6 | |
5 | 3, 4 | syl6ibr 151 | . . . . 5 |
6 | dftp2 3419 | . . . . . 6 | |
7 | 6 | eleq2i 2104 | . . . . 5 |
8 | 5, 7 | syl6ibr 151 | . . . 4 |
9 | eleq1 2100 | . . . 4 | |
10 | 8, 9 | mpbidi 140 | . . 3 |
11 | 10 | exlimdv 1700 | . 2 |
12 | 1, 11 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 884 wceq 1243 wex 1381 wcel 1393 cab 2026 ctp 3377 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-tp 3383 |
This theorem is referenced by: (None) |
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