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Mirrors > Home > MPE Home > Th. List > sorpssi | Structured version Visualization version Unicode version |
Description: Property of a chain of sets. (Contributed by Stefan O'Rear, 2-Nov-2014.) |
Ref | Expression |
---|---|
sorpssi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | solin 4796 |
. . 3
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2 | elex 3065 |
. . . . . 6
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3 | 2 | ad2antll 740 |
. . . . 5
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4 | brrpssg 6599 |
. . . . 5
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5 | 3, 4 | syl 17 |
. . . 4
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6 | biidd 245 |
. . . 4
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7 | elex 3065 |
. . . . . 6
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8 | 7 | ad2antrl 739 |
. . . . 5
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9 | brrpssg 6599 |
. . . . 5
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10 | 8, 9 | syl 17 |
. . . 4
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11 | 5, 6, 10 | 3orbi123d 1347 |
. . 3
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12 | 1, 11 | mpbid 215 |
. 2
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13 | sspsstri 3546 |
. 2
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14 | 12, 13 | sylibr 217 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-pss 3431 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-br 4416 df-opab 4475 df-so 4774 df-xp 4858 df-rel 4859 df-rpss 6597 |
This theorem is referenced by: sorpssun 6604 sorpssin 6605 sorpssuni 6606 sorpssint 6607 sorpsscmpl 6608 enfin2i 8776 fin1a2lem9 8863 fin1a2lem10 8864 fin1a2lem11 8865 fin1a2lem13 8867 |
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