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Mirrors > Home > ILE Home > Th. List > xnn0nnn0pnf | Unicode version |
Description: An extended nonnegative integer which is not a standard nonnegative integer is positive infinity. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
xnn0nnn0pnf | NN0* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxnn0 9173 | . . 3 NN0* | |
2 | pm2.53 712 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 NN0* |
4 | 3 | imp 123 | 1 NN0* |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 698 wceq 1342 wcel 2135 cpnf 7924 cn0 9108 NN0*cxnn0 9171 |
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-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4097 ax-pow 4150 ax-un 4408 ax-cnex 7838 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2726 df-un 3118 df-in 3120 df-ss 3127 df-pw 3558 df-sn 3579 df-pr 3580 df-uni 3787 df-pnf 7929 df-xr 7931 df-xnn0 9172 |
This theorem is referenced by: (None) |
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