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Mirrors > Home > MPE Home > Th. List > ssin | Structured version Visualization version Unicode version |
Description: Subclass of intersection. Theorem 2.8(vii) of [Monk1] p. 26. (Contributed by NM, 15-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ssin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3629 |
. . . . 5
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2 | 1 | imbi2i 318 |
. . . 4
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3 | 2 | albii 1702 |
. . 3
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4 | jcab 879 |
. . . 4
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5 | 4 | albii 1702 |
. . 3
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6 | 19.26 1743 |
. . 3
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7 | 3, 5, 6 | 3bitrri 280 |
. 2
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8 | dfss2 3433 |
. . 3
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9 | dfss2 3433 |
. . 3
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10 | 8, 9 | anbi12i 708 |
. 2
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11 | dfss2 3433 |
. 2
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12 | 7, 10, 11 | 3bitr4i 285 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-v 3059 df-in 3423 df-ss 3430 |
This theorem is referenced by: ssini 3667 ssind 3668 uneqin 3706 disjpss 3827 trin 4521 pwin 4757 fin 5786 wfrlem4 7065 epfrs 8241 tcmin 8251 resscntz 17034 subgdmdprd 17716 tgval 20019 eltg3i 20025 innei 20190 cnprest2 20355 subislly 20545 lly1stc 20560 xkohaus 20717 xkoinjcn 20751 opnfbas 20906 supfil 20959 rnelfm 21017 tsmsres 21207 restmetu 21634 chabs2 27219 cmbr4i 27303 pjin3i 27896 mdbr2 27998 dmdbr2 28005 dmdbr5 28010 mdslle1i 28019 mdslle2i 28020 mdslj1i 28021 mdslj2i 28022 mdsl2i 28024 mdslmd1lem1 28027 mdslmd1lem2 28028 mdslmd1i 28031 mdslmd3i 28034 hatomistici 28064 chrelat2i 28067 cvexchlem 28070 mdsymlem1 28105 mdsymlem3 28107 mdsymlem6 28110 dmdbr5ati 28124 pnfneige0 28806 ballotlem2 29370 iccllyscon 30022 frrlem4 30566 heibor1lem 32186 dochexmidlem1 35073 superficl 36216 |
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