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Mirrors > Home > ILE Home > Th. List > ssexi | Unicode version |
Description: The subset of a set is also a set. (Contributed by NM, 9-Sep-1993.) |
Ref | Expression |
---|---|
ssexi.1 | |
ssexi.2 |
Ref | Expression |
---|---|
ssexi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssexi.2 | . 2 | |
2 | ssexi.1 | . . 3 | |
3 | 2 | ssex 4035 | . 2 |
4 | 1, 3 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 wss 3041 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 |
This theorem is referenced by: zfausab 4040 pp0ex 4083 ord3ex 4084 epse 4234 opabex 5612 oprabex 5994 phplem2 6715 phpm 6727 snexxph 6806 sbthlem2 6814 niex 7088 enqex 7136 enq0ex 7215 npex 7249 ltnqex 7325 gtnqex 7326 recexprlemell 7398 recexprlemelu 7399 enrex 7513 axcnex 7635 peano5nnnn 7668 reex 7722 nnex 8694 zex 9031 qex 9392 ixxex 9650 serclim0 11042 climle 11071 iserabs 11212 isumshft 11227 explecnv 11242 prmex 11721 exmidunben 11866 istopon 12107 dmtopon 12117 lmres 12344 climcncf 12667 reldvg 12744 |
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