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Mirrors > Home > ILE Home > Th. List > otth2 | Unicode version |
Description: Ordered triple theorem, with triple express with ordered pairs. (Contributed by NM, 1-May-1995.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
otth.1 |
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otth.2 |
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otth.3 |
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Ref | Expression |
---|---|
otth2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | otth.1 |
. . . 4
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2 | otth.2 |
. . . 4
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3 | 1, 2 | opth 4028 |
. . 3
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4 | 3 | anbi1i 446 |
. 2
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5 | 1, 2 | opex 4020 |
. . 3
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6 | otth.3 |
. . 3
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7 | 5, 6 | opth 4028 |
. 2
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8 | df-3an 922 |
. 2
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9 | 4, 7, 8 | 3bitr4i 210 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 4000 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2614 df-un 2988 df-in 2990 df-ss 2997 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 |
This theorem is referenced by: otth 4033 oprabid 5616 eloprabga 5670 |
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