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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 3321 |
. 2
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2 | df-3an 981 |
. . 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 3760 |
. . . 4
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6 | tpss.3 |
. . . . 5
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7 | 6 | snss 3739 |
. . . 4
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8 | 5, 7 | anbi12i 460 |
. . 3
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9 | 2, 8 | bitri 184 |
. 2
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10 | df-tp 3612 |
. . 3
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11 | 10 | sseq1i 3193 |
. 2
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12 | 1, 9, 11 | 3bitr4i 212 |
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-3an 981 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-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-tp 3612 |
This theorem is referenced by: (None) |
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