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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 |
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ssexi.1 |
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ssexi.2 |
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Ref | Expression |
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ssexi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssexi.2 |
. 2
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2 | ssexi.1 |
. . 3
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3 | 2 | ssex 4137 |
. 2
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4 | 1, 3 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4118 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 |
This theorem is referenced by: zfausab 4142 pp0ex 4186 ord3ex 4187 epse 4339 opabex 5736 mptexw 6108 oprabex 6123 mpoexw 6208 phplem2 6847 phpm 6859 snexxph 6943 sbthlem2 6951 2omotaplemst 7247 niex 7299 enqex 7347 enq0ex 7426 npex 7460 ltnqex 7536 gtnqex 7537 recexprlemell 7609 recexprlemelu 7610 enrex 7724 axcnex 7846 peano5nnnn 7879 reex 7933 nnex 8911 zex 9248 qex 9618 ixxex 9883 iccen 9990 serclim0 11294 climle 11323 iserabs 11464 isumshft 11479 explecnv 11494 prodfclim1 11533 prmex 12093 exmidunben 12407 istopon 13171 dmtopon 13181 lmres 13408 climcncf 13731 reldvg 13808 |
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