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Mirrors > Home > MPE Home > Th. List > ssdisj | Structured version Unicode version |
Description: Intersection with a subclass of a disjoint class. (Contributed by FL, 24-Jan-2007.) |
Ref | Expression |
---|---|
ssdisj |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3776 |
. . . 4
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2 | ssrin 3684 |
. . . . 5
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3 | sstr2 3472 |
. . . . 5
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4 | 2, 3 | syl 16 |
. . . 4
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5 | 1, 4 | syl5bir 218 |
. . 3
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6 | 5 | imp 429 |
. 2
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7 | ss0 3777 |
. 2
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8 | 6, 7 | syl 16 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-v 3080 df-dif 3440 df-in 3444 df-ss 3451 df-nul 3747 |
This theorem is referenced by: djudisj 5374 fimacnvdisj 5698 marypha1lem 7795 ackbij1lem16 8516 ackbij1lem18 8518 fin23lem20 8618 fin23lem30 8623 elcls3 18820 neindisj 18854 imadifxp 26091 diophren 29301 |
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