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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 3309 |
. 2
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2 | df-3an 980 |
. . 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 3748 |
. . . 4
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6 | tpss.3 |
. . . . 5
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7 | 6 | snss 3727 |
. . . 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 3600 |
. . 3
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11 | 10 | sseq1i 3181 |
. 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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-tp 3600 |
This theorem is referenced by: (None) |
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