Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pnf0xnn0 | Unicode version |
Description: Positive infinity is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
pnf0xnn0 | NN0* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2139 | . . 3 | |
2 | 1 | olci 721 | . 2 |
3 | elxnn0 9042 | . 2 NN0* | |
4 | 2, 3 | mpbir 145 | 1 NN0* |
Colors of variables: wff set class |
Syntax hints: wo 697 wceq 1331 wcel 1480 cpnf 7797 cn0 8977 NN0*cxnn0 9040 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-un 4355 ax-cnex 7711 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-uni 3737 df-pnf 7802 df-xr 7804 df-xnn0 9041 |
This theorem is referenced by: inftonninf 10214 |
Copyright terms: Public domain | W3C validator |