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Mirrors > Home > ILE Home > Th. List > ssexg | Unicode version |
Description: The subset of a set is also a set. Exercise 3 of [TakeutiZaring] p. 22 (generalized). (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
ssexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq2 3021 | . . . 4 | |
2 | 1 | imbi1d 229 | . . 3 |
3 | vex 2604 | . . . 4 | |
4 | 3 | ssex 3915 | . . 3 |
5 | 2, 4 | vtoclg 2658 | . 2 |
6 | 5 | impcom 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 cvv 2601 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 df-ss 2986 |
This theorem is referenced by: ssexd 3918 difexg 3919 rabexg 3921 elssabg 3923 elpw2g 3931 abssexg 3955 snexg 3956 sess1 4092 sess2 4093 trsuc 4177 unexb 4195 uniexb 4223 xpexg 4470 riinint 4611 dmexg 4614 rnexg 4615 resexg 4668 resiexg 4673 imaexg 4700 exse2 4719 cnvexg 4875 coexg 4882 fabexg 5097 f1oabexg 5158 relrnfvex 5213 fvexg 5214 sefvex 5216 mptfvex 5277 mptexg 5407 ofres 5745 resfunexgALT 5757 cofunexg 5758 fnexALT 5760 f1dmex 5763 oprabexd 5774 mpt2exxg 5853 tposexg 5896 frecabex 6007 erex 6153 ssdomg 6281 fiprc 6315 shftfvalg 9706 shftfval 9709 |
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