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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. (Contributed by Jim Kingdon, 10-Aug-2018.) |
Ref | Expression |
---|---|
sssnr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3249 |
. . 3
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2 | sseq1 2960 |
. . 3
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3 | 1, 2 | mpbiri 157 |
. 2
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4 | eqimss 2991 |
. 2
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5 | 3, 4 | jaoi 635 |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-dif 2914 df-in 2918 df-ss 2925 df-nul 3219 |
This theorem is referenced by: pwsnss 3565 |
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