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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 3111 |
. 2
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2 | df-3an 886 |
. . 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 3511 |
. . . 4
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6 | tpss.3 |
. . . . 5
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7 | 6 | snss 3485 |
. . . 4
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8 | 5, 7 | anbi12i 433 |
. . 3
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9 | 2, 8 | bitri 173 |
. 2
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10 | df-tp 3375 |
. . 3
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11 | 10 | sseq1i 2963 |
. 2
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12 | 1, 9, 11 | 3bitr4i 201 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-tp 3375 |
This theorem is referenced by: (None) |
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