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Mirrors > Home > ILE Home > Th. List > sssnr | Unicode version |
Description: Empty set and the singleton itself are subsets of a singleton. Concerning the converse, see exmidsssn 4040. (Contributed by Jim Kingdon, 10-Aug-2018.) |
Ref | Expression |
---|---|
sssnr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3325 |
. . 3
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2 | sseq1 3048 |
. . 3
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3 | 1, 2 | mpbiri 167 |
. 2
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4 | eqimss 3079 |
. 2
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5 | 3, 4 | jaoi 672 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-dif 3002 df-in 3006 df-ss 3013 df-nul 3288 |
This theorem is referenced by: pwsnss 3653 |
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