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Mirrors > Home > ILE Home > Th. List > tpid3g | Unicode version |
Description: Closed theorem form of tpid3 3720. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tpid3g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2763 |
. 2
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2 | 3mix3 1169 |
. . . . . . 7
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3 | 2 | a1i 9 |
. . . . . 6
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4 | abid 2175 |
. . . . . 6
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5 | 3, 4 | imbitrrdi 162 |
. . . . 5
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6 | dftp2 3653 |
. . . . . 6
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7 | 6 | eleq2i 2254 |
. . . . 5
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8 | 5, 7 | imbitrrdi 162 |
. . . 4
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9 | eleq1 2250 |
. . . 4
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10 | 8, 9 | mpbidi 151 |
. . 3
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11 | 10 | exlimdv 1829 |
. 2
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12 | 1, 11 | mpd 13 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3or 980 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-sn 3610 df-pr 3611 df-tp 3612 |
This theorem is referenced by: rngmulrg 12611 srngmulrd 12622 lmodscad 12640 ipsmulrd 12652 ipsipd 12655 topgrptsetd 12672 |
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