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Mirrors > Home > ILE Home > Th. List > 0ss | Unicode version |
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
0ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3228 | . . 3 | |
2 | 1 | pm2.21i 575 | . 2 |
3 | 2 | ssriv 2949 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 wss 2917 c0 3224 |
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 df-nul 3225 |
This theorem is referenced by: ss0b 3256 0pss 3265 npss0 3266 ssdifeq0 3305 sssnr 3524 ssprr 3527 uni0 3607 int0el 3645 0disj 3761 disjx0 3763 tr0 3865 0elpw 3917 fr0 4088 elnn 4328 rel0 4462 0ima 4685 fun0 4957 f0 5080 oaword1 6050 bdeq0 9987 bj-omtrans 10081 |
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