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Mirrors > Home > MPE 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 4403 |
. . 3
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4 | 3 | anbi1i 677 |
. 2
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5 | opex 4395 |
. . 3
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6 | otth.3 |
. . 3
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7 | 5, 6 | opth 4403 |
. 2
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8 | df-3an 938 |
. 2
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9 | 4, 7, 8 | 3bitr4i 269 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: otth 4408 oprabid 6072 eloprabga 6127 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 ax-sep 4298 ax-nul 4306 ax-pr 4371 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-ne 2577 df-rab 2683 df-v 2926 df-dif 3291 df-un 3293 df-in 3295 df-ss 3302 df-nul 3597 df-if 3708 df-sn 3788 df-pr 3789 df-op 3791 |
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