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Mirrors > Home > MPE Home > Th. List > sscon | Structured version Unicode version |
Description: Contraposition law for subsets. Exercise 15 of [TakeutiZaring] p. 22. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
sscon |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3459 |
. . . . 5
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2 | 1 | con3d 133 |
. . . 4
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3 | 2 | anim2d 565 |
. . 3
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4 | eldif 3447 |
. . 3
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5 | eldif 3447 |
. . 3
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6 | 3, 4, 5 | 3imtr4g 270 |
. 2
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7 | 6 | ssrdv 3471 |
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 |
This theorem is referenced by: sscond 3602 sorpsscmpl 6482 sbthlem1 7532 sbthlem2 7533 cantnfp1lem1 7998 cantnfp1lem3 8000 cantnfp1lem1OLD 8024 cantnfp1lem3OLD 8026 isf34lem7 8660 isf34lem6 8661 setsres 14321 mplsubglem 17635 mplsubglemOLD 17637 cctop 18743 clsval2 18787 ntrss 18792 hauscmplem 19142 ptbasin 19283 cfinfil 19599 csdfil 19600 uniioombllem5 21201 kur14lem6 27244 dvasin 28629 bj-2upln1upl 32850 |
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