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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 2939 | . . . . 5 | |
2 | 1 | con3d 561 | . . . 4 |
3 | 2 | anim2d 320 | . . 3 |
4 | eldif 2927 | . . 3 | |
5 | eldif 2927 | . . 3 | |
6 | 3, 4, 5 | 3imtr4g 194 | . 2 |
7 | 6 | ssrdv 2951 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wcel 1393 cdif 2914 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 |
This theorem is referenced by: sscond 3080 |
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