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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 4119 |
. . 3
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4 | 3 | anbi1i 451 |
. 2
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5 | 1, 2 | opex 4111 |
. . 3
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6 | otth.3 |
. . 3
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7 | 5, 6 | opth 4119 |
. 2
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8 | df-3an 947 |
. 2
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9 | 4, 7, 8 | 3bitr4i 211 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 |
This theorem is referenced by: otth 4124 oprabid 5757 eloprabga 5812 |
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