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Mirrors > Home > ILE Home > Th. List > sscon | Unicode version |
Description: Contraposition law for subsets. Exercise 15 of [TakeutiZaring] p. 22. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
sscon |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3091 | . . . . 5 | |
2 | 1 | con3d 620 | . . . 4 |
3 | 2 | anim2d 335 | . . 3 |
4 | eldif 3080 | . . 3 | |
5 | eldif 3080 | . . 3 | |
6 | 3, 4, 5 | 3imtr4g 204 | . 2 |
7 | 6 | ssrdv 3103 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wcel 1480 cdif 3068 wss 3071 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 |
This theorem is referenced by: sscond 3213 sbthlem1 6845 sbthlem2 6846 |
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