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Mirrors > Home > MPE Home > Th. List > snsspr1 | Structured version Visualization version Unicode version |
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.) |
Ref | Expression |
---|---|
snsspr1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3776 | . 2 | |
2 | df-pr 4180 | . 2 | |
3 | 1, 2 | sseqtr4i 3638 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cun 3572 wss 3574 csn 4177 cpr 4179 |
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 |
This theorem is referenced by: snsstp1 4347 op1stb 4940 uniop 4977 rankopb 8715 ltrelxr 10099 2strbas 15984 2strbas1 15987 phlvsca 16038 prdshom 16127 ipobas 17155 ipolerval 17156 lspprid1 18997 lsppratlem3 19149 lsppratlem4 19150 ex-dif 27280 ex-un 27281 ex-in 27282 coinflippv 30545 subfacp1lem2a 31162 altopthsn 32068 rankaltopb 32086 dvh3dim3N 36738 mapdindp2 37010 lspindp5 37059 algsca 37751 clsk1indlem2 38340 clsk1indlem3 38341 clsk1indlem1 38343 gsumpr 42139 |
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