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Mirrors > Home > ILE Home > Th. List > snexg | Unicode version |
Description: A singleton whose element
exists is a set. The ![]() ![]() ![]() |
Ref | Expression |
---|---|
snexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwexg 4112 |
. 2
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2 | snsspw 3699 |
. . 3
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3 | ssexg 4075 |
. . 3
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4 | 2, 3 | mpan 421 |
. 2
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5 | 1, 4 | syl 14 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 |
This theorem is referenced by: snex 4117 notnotsnex 4119 exmidsssnc 4134 snelpwi 4142 opexg 4158 opm 4164 tpexg 4373 op1stbg 4408 sucexb 4421 elxp4 5034 elxp5 5035 opabex3d 6027 opabex3 6028 1stvalg 6048 2ndvalg 6049 mpoexxg 6116 cnvf1o 6130 brtpos2 6156 tfr0dm 6227 tfrlemisucaccv 6230 tfrlemibxssdm 6232 tfrlemibfn 6233 tfr1onlemsucaccv 6246 tfr1onlembxssdm 6248 tfr1onlembfn 6249 tfrcllemsucaccv 6259 tfrcllembxssdm 6261 tfrcllembfn 6262 fvdiagfn 6595 ixpsnf1o 6638 mapsnf1o 6639 xpsnen2g 6731 zfz1isolem1 10615 climconst2 11092 ennnfonelemp1 11955 setsvalg 12028 setsex 12030 setsslid 12048 strle1g 12088 1strbas 12097 |
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