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Mirrors > Home > ILE Home > Th. List > tpss | Unicode version |
Description: A triplet of elements of a class is a subset of the class. (Contributed by NM, 9-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
tpss.1 |
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tpss.2 |
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tpss.3 |
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Ref | Expression |
---|---|
tpss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unss 3214 |
. 2
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2 | df-3an 945 |
. . 3
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3 | tpss.1 |
. . . . 5
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4 | tpss.2 |
. . . . 5
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5 | 3, 4 | prss 3640 |
. . . 4
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6 | tpss.3 |
. . . . 5
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7 | 6 | snss 3613 |
. . . 4
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8 | 5, 7 | anbi12i 453 |
. . 3
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9 | 2, 8 | bitri 183 |
. 2
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10 | df-tp 3499 |
. . 3
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11 | 10 | sseq1i 3087 |
. 2
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12 | 1, 9, 11 | 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 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-sn 3497 df-pr 3498 df-tp 3499 |
This theorem is referenced by: (None) |
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