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Mirrors > Home > MPE Home > Th. List > snsstp2 | Structured version Visualization version Unicode version |
Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.) |
Ref | Expression |
---|---|
snsstp2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snsspr2 4346 | . . 3 | |
2 | ssun1 3776 | . . 3 | |
3 | 1, 2 | sstri 3612 | . 2 |
4 | df-tp 4182 | . 2 | |
5 | 3, 4 | sseqtr4i 3638 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cun 3572 wss 3574 csn 4177 cpr 4179 ctp 4181 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-pr 4180 df-tp 4182 |
This theorem is referenced by: fr3nr 6979 rngplusg 16002 srngplusg 16010 lmodplusg 16019 ipsaddg 16026 ipsvsca 16029 phlplusg 16036 topgrpplusg 16044 otpstset 16053 otpstsetOLD 16057 odrngplusg 16068 odrngle 16071 prdsplusg 16118 prdsvsca 16120 prdsle 16122 imasplusg 16177 imasvsca 16180 imasle 16183 fuchom 16621 setchomfval 16729 catchomfval 16748 estrchomfval 16766 xpchomfval 16819 psrplusg 19381 psrvscafval 19390 cnfldadd 19751 cnfldle 19755 trkgdist 25345 algaddg 37749 clsk1indlem4 38342 rngchomfvalALTV 41984 ringchomfvalALTV 42047 |
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