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Mirrors > Home > ILE Home > Th. List > 0xnn0 | Unicode version |
Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
0xnn0 | NN0* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssxnn0 9188 | . 2 NN0* | |
2 | 0nn0 9137 | . 2 | |
3 | 1, 2 | sselii 3144 | 1 NN0* |
Colors of variables: wff set class |
Syntax hints: wcel 2141 cc0 7761 cn0 9122 NN0*cxnn0 9185 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-1cn 7854 ax-icn 7856 ax-addcl 7857 ax-mulcl 7859 ax-i2m1 7866 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-n0 9123 df-xnn0 9186 |
This theorem is referenced by: 0tonninf 10382 |
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