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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 3362 | . . 3 | |
2 | 1 | pm2.21i 635 | . 2 |
3 | 2 | ssriv 3096 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 wss 3066 c0 3358 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-dif 3068 df-in 3072 df-ss 3079 df-nul 3359 |
This theorem is referenced by: ss0b 3397 ssdifeq0 3440 sssnr 3675 ssprr 3678 uni0 3758 int0el 3796 0disj 3921 disjx0 3923 tr0 4032 0elpw 4083 exmidsssn 4120 fr0 4268 elnn 4514 rel0 4659 0ima 4894 fun0 5176 f0 5308 oaword1 6360 0domg 6724 nnnninf 7016 exmidfodomrlemim 7050 sum0 11150 ennnfonelemj0 11903 ennnfonelemkh 11914 0opn 12162 baspartn 12206 0cld 12270 ntr0 12292 bdeq0 13054 bj-omtrans 13143 el2oss1o 13177 nninfsellemsuc 13197 |
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